JEE  >  Maths 35 Years JEE Main & Advanced Past year Papers  >  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Document Description: Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The notes and questions for Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced have been prepared according to the JEE exam syllabus. Information about Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced covers topics like and Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced.

Introduction of Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced in English is available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced in Hindi for Maths 35 Years JEE Main & Advanced Past year Papers course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
1 Crore+ students have signed up on EduRev. Have you?

DIRECTIONS (Q. 1-6) :  Each question contains statements given in two columns, which have to be matched. The statements in Column-I are labelled A, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example :

If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s then the correct darkening of bubbles will look like the given.

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 1. Match the following :

(A) Two rays x + y = |a| and ax – y = 1 intersects each other in the                       (p) 2
 first quadrant in the interval a ∈ (a0, ∞), the value of a0 is

(B) Point (α , β , γ) lies on the plane x + y + z = 2.                                                     (q) 4/3

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(C)  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                                                                                    (r) Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(D) If sinA sinB sinC + cosA cosB = 1, then the value of sinC =                             (s) 1

Ans. (A) → s; (B) → p; (C) → r, q; (D) → s

Solution. (A) On solving the given equations x + y = |a| and ax – y = 1, we get

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Rays intersect each other in I quad.
 

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
(B) (α, β, γ) lies on the plane x + y + z = 2
⇒ α + β + γ = 2

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

i.e., y2 = (x + 1) represent same area under the given limits]

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(D) Given : sin A sin B sin C + cos A cos B = 1

But sin A sin B sin C + cos A cos B < sin A sin B + cos

A cos B = cos (A – B)

⇒ cos (A – B) > 1  ⇒ cos (A – B) =1
⇒ A – B  = 0 ⇒ A = B

∴ Given relation becomes sin2A sin C + cos2 A = 1

⇒ sin C = 1,

(D) → (s)


Q. 2. Consider the following linear equations ax + by + cz = 0; bx + cy + az = 0;    cx + ay + bz = 0 

Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I                                                                                                 Column II

(A) a + b + c ≠ 0 and a2 + b2 + c2 = ab + bc + ca                                (p) the equations represent planes meeting only at asingle point

(B) a + b + c = 0 and a2 + b2 + c2 ≠ ab + bc + ca                               (q) the equations represent the line x = y = z.

(C) a + b + c ≠ 0 and a2 + b2 + c2 ≠ ab + bc + ca                               (r) the equations represent identical planes.

(D) a + b + c = 0 and a2 + b2 + c2 = ab + bc + ca                               (s) the equations represent the whole of the three dimensional space.

Ans. (A) → r; (B) → q; (C) → p; (D) → s

Solution. Here we have, the determinant of the coefficient matrix of given equation, as

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

This equation represent identical planes.

(B) a +b +c = 0 and a2 + b2+ c2 - ab - bc - ca ≠ 0

⇒ Δ = 0 and a, b, c are not all equal.

∴ All equations are not identical but have infinite many solutions.

∴ ax + by = (a+ b)z (using a+b+c = 0) and bx + cy = (b+ c)z

⇒ (b2 - ac) y = (b2- ac)z ⇒ y = z

⇒ ax + by + cy= 0 ⇒ ax = ay ⇒ x = y

⇒ x = y = z 

∴ The equations represent the line x = y = z

(C) a + b + c ≠ 0 and a2 + b2+ c2 - ab - bc - ca ≠ 0

⇒ Δ ≠ 0 ⇒ Equations have only trivial solution i.e., x = y = z = 0

∴ the equations represents the three planes meeting at a single point namely origin.

(D) a +b +c= 0 and a+ b2+ c2 - ab - bc - ca = 0

⇒ a = b = c and Δ = 0 ⇒ a = b = c = 0

⇒ All equations are satisfied by all x, y, and z.

⇒ The equations represent the whole of the three dimensional space (all points in 3–D)


Q. 3. Match the statements / expressions given in Column-I with the values given in Column-II.

Column-I                                                                                             Column-II

(A) Root(s) of the equation 2 sin2 θ  + sin2 2θ  = 2                                (p) π/6

(B) Points of discontinuity of the  unction Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE         (q) π/4
f where [y] denotes the largest  integer less than or equal to y

(C) Volume of the parallelopiped with its edges  represented by       (r) π/3
 the vectors  
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(D) Angle between vector  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are unit vectors      (s) π/2
satisfying  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE   

                                                                                                                     (t) π

Ans. A → q,s; B → p,r,s, t; C → t; D→ r

Solution.

(A) The given equation is

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(B) We know that [x] is discontinuous at all integral values, therefore  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE discontinuous at Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and π. Also  cos  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE for any of these values of x.

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is discontinuous at Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE    and π.

(C) We know that th e volume of a par allelopipe with coterminus edges as  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is given by  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ The required volume is   Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(where θ is the angle between  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE )
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 4. Match the statements/expressions given in Column-I with the values given in Column-II.

Column-I                                                                                         Column-II

(A) The number of solutions of the equation                                       (p) 1

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(B) Value(s) of k  for which the planes k x + 4y + z = 0,                        (q) 2
 4x + k y + 2z = 0 and 2x + 2y + z = 0 intersect in a straight line

(C) Value(s) of k  for which | x – 1 | + | x – 2 | + | x + 1 |                        (r) 3
 | + | x + 2 | = 4k has integer solution(s)

(D) If  y' = y + 1 and y (0) = 1, then value(s) of y (1n 2)                          (s) 4

                                                                                                                    (t) 5

Ans. A → p;B → q, s;C → q, r, s, t;D→ r

Solution. (A) For the solution of  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Let us consider two functions

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

The range of  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE also it is an increasing function on  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE Their graph are as shown in the figure below :

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Clearly the two curves meet only at one point, therefore the given equation has only one solution in Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(B) Three given planes are

kx + 4 y +z = 0
4x + ky + 2z = 0
2x + 2 y +z = 0

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Clearly all the planes pass through (0,0,0).

∴ Their line of intersection also pass through (0, 0, 0) Let a, b, c, be the direction ratios of required line, then we should have

ka + 4b +c = 0
4a + kb + 2c = 0
2a + 2b +c = 0

For the required line to exist the above system of equations in a, b, c, should have non trivial solution i.e.

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

The graph of the above function is as given below

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
(D) Given that

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 5. Match the statement in Column-1 with the values in Column -II

Column – I                                                                                               Column – II

(A) A line from the origin meets the lines  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE             (p) – 4
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and at P and Q respectively..

If length PQ = d, then d2 is

(B) The values of x satisfying                                                                   (q) 0

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(C) Non-zero vectors  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                                        (r) 4
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE , then the possible values of μ are

(D) Let f be the function on [–π, π] given by f (0) = 9                             (s) 5

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Ans. (A) → t; (B) → p, r; (C) → q, s; (D) → r

Solution. Let the line through origin be   Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  — (1)

then as it intersects

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE      —(2)
and Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE          —(3)

at P and Q, shortest distance of (1) with (2) and (3) should be zero.

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solving (4) and (5), we get

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Hence equation (1) becomes  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

For some value of Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

which lies on (2) also

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Also for some value of  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

which lies on (3) also

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

From (1) and (2), we get

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEMatrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 6.  Match the statements given in Column-I with the values given in Column-II.

Column-I                                                                                             Column-II

(A)  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE form                                     (p) π/6
 a triangle, then the internal angle of the triangle
 between Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(B)  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                     (q) 2π/3

(C)  The value of  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                                                      (r) π/3

(D) The maximum value of  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                          (s) π
 is given by

                                                                                                                   (t) π/2

Ans. A→q, B→p, C→s, D→t

Solution.  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ The figure is as shown.

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Clearly max.  Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEbut will not be attained.

∴ D → t.

The document Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.
All you need of JEE at this link: JEE

Related Searches

ppt

,

Free

,

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

pdf

,

MCQs

,

practice quizzes

,

study material

,

Objective type Questions

,

shortcuts and tricks

,

Extra Questions

,

video lectures

,

Viva Questions

,

Exam

,

Summary

,

Sample Paper

,

Semester Notes

,

past year papers

,

Important questions

,

mock tests for examination

,

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

Previous Year Questions with Solutions

,

Matrix-Match Type Questions: Vector Algebra and Three Dimensional Geometry - 1 | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

;