JEE Exam  >  JEE Tests  >  Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - JEE MCQ

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - JEE MCQ


Test Description

30 Questions MCQ Test - Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry for JEE 2024 is part of JEE preparation. The Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry questions and answers have been prepared according to the JEE exam syllabus.The Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry below.
Solutions of Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry questions in English are available as part of our course for JEE & Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry solutions in Hindi for JEE course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry | 82 questions in 160 minutes | Mock test for JEE preparation | Free important questions MCQ to study for JEE Exam | Download free PDF with solutions
Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 1

A plane which passes through the point (3, 2, 0) and the line

 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 1

As the point (3, 2, 0)  lies on the given line

∴ There can be infinite many planes passing through this line. But here out of the four options only first option is satisfied by the coordinates of both the points (3, 2, 0) and (4, 7, 4)
∴ x – y + z = 1 is the required plane.

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 2

 and the angle between   then   is equal to

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 2

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 3

 are vectors such that   then

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 3



Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 4

 are vectors show that   and 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 4


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 5

thus what will be the value of   given that 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 5


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 6

If the vectors  are such that   form a right handed system then 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 6

Since   form a right handed system,

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 7

 and   are two vectors and   a vector such that

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 7

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 8

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 8

Above three conditions will be satisfied for non-zero vectors if and only if

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 9

The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π /4 with plane  x + y = 3 are

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 9

Equation of plane through (1, 0, 0) is a (x – 1) + by + cz = 0 ...(i)
(i) passes through (0, 1, 0). –a + b = 0 ⇒ b = a; Also, cos 45°

So d.r of normal are a, a 

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 10

Let  is a unit vector such that  is equal to

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 10

since  perpendicular  

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 11

A particle acted on by constant forces   and   is displaced from the point   to the point  The total work done by the forces is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 11

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 12

The vectors  are the sides of a triangle ABC. The length of the median through A is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 12


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 13

The shortest distance from the plane 12x + 4 y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155 is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 13

Shortest distance = perpendicular distance between the plane and sphere = distance of plane from centre of sphere – radius

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 14

The two lines x = ay + b , z = cy + d and x = a`y + b`, z = c`y + d` will be perpendicular, if and only if

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 14

For perpendicularity of lines  aa'+1 + cc' = 0

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 15

The lines  arecoplanar if

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 15


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 16

 are 3 vectors, such that  ,  then   is equal to

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 16

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 17

The radius of the circle in which the sphere

x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0  is  cut  by  the plane x + 2y + 2z + 7 = 0 is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 17

Centre of sphere = (–1, 1, 2) Radius of sphere 

Perpendicular distance from centre to the plane

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 18

A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1) B(2, 1, 3) and C(–1, 1, 2). Then the angle between the faces OAB  and ABC will be

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 18

Vector perpendicular to the face OAB

Vector perpendicular  to the face ABC

Angle between the faces  = angle between their normals

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 19

and vectrs (1, a,a2),(1, b, b2) and (1, c,c2) are non- coplanar, then the product abc equals

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 19



Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 20

Consider points A , B , C and D with position vectors   and respectively. Then ABCD is a

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 20

∴ None of the options is satisfied

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 21

If  are three non - coplanar vectors, then  equals

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 21


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 22

Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a' , b' , c' from the origin then

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 22

Eq. of planes be 

(⊥ r distance on plane from origin is same.)

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 23

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y +4z + 5 = 0 is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 23

The planes ar e 2x + y + 2z - 8=0 . ...(1)
and 4x + 2y + 4z + 5 = 0

          ...(2)

∴ Distance  between (1) and (2)

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 24

A line with direction cosin es proportional to 2, 1, 2 meets each of the lines x = y + a = z an d x + a = 2y = 2z . The co-ordinates of each of the points of intersection are given by

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 24

Let a point on th e lin e x = y + a = z is
(λ, λ - a,λ) and a point on th e lin e x + a = 2 y = 2z

 then direction ratio of the line joining these poin ts are

If it respresents the required line, then

on solving we get λ = 3a, μ = 2a
∴ The required points of intersection are (3a, 3aa,3a) and 

or (3a, 2a, 3a) and (a,a,a)

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 25

If the straight lines

with parameters s and t respectively, are co-planar, then λ equals.

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 25

The given lines are

The lines are coplanar, if


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 26

The intersection of the spheres

x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 -3x + 3y + 4z = 8

is the same as the intersection of one of the sphere and the plane

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 26

The equation s of spheres are

S1 : x2 + y2 + z2 + 7x - 2y - z -13 = 0 and

S2 : x2 + y2 + z- 3x + 3y + 4z-8 = 0

Their plane of intersection is

S1 - S2 = 0 ⇒ 10x - 5y - 5z - 5 = 0
⇒ 2x- y-z = 1

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 27

 be three non -zero vectors such that no two of these are collinear. If the vector   is collinear with   is collinear with   (λ being some non-zero scalar) then equals

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 27

Let   wh ere t and s are scalars. Adding, we get


Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 28

A particles is acted upon by constant forces  and   which displace it from a point   to  the point  The work done in standard units by the forces is given by

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 28

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 29

If    are non-coplanar vectors and l is a real number, then the vectors    are non coplanar for

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 29


coplanar if 

 ∵ Forces are noncoplanar for all λ, except 

Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 30

 be such that   If the projection   is equal to that of    and   are perpendicular to each other then 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry - Question 30



View more questions
Information about Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry Page
In this test you can find the Exam questions for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry solved & explained in the simplest way possible. Besides giving Questions and answers for Test: 35 Year JEE Previous Year Questions: Vector Algebra and Three Dimensional Geometry, EduRev gives you an ample number of Online tests for practice

Top Courses for JEE

Download as PDF

Top Courses for JEE