JEE  >  Maths 35 Years JEE Main & Advanced Past year Papers  >  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced

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

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

Introduction of Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced in English is available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | 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: Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
1 Crore+ students have signed up on EduRev. Have you?

Q. 1. If  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are vectors in space given by  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE then find the value of  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEInteger Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE          (2010)

Ans. 5

Solution.

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

Q. 2. If the distance between the plane Ax – 2y + z = d and the plane containing the lines  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE, then find |d|.             (2010)

Ans. 6

Solution. The equation of plane containing the lines

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

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

∴ Distance between x – 2 y +z=0 and Ax –2 y + z = d

= Perpendicular distance between parallel planes  (∴ A= 1)

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

Q. 3. Let  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE be three given vectors.   Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a vector such that  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE then the value of  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (2011)

Ans. 9

Solution.

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


Q. 4. If Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEare unit vectors satisfying Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (2012)

Ans. 3

Solution.  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are units vectors such that 

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

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

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


Q. 5. Consider the set of eight vectors Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE Three non- coplanar vectors can be chosen from V in 2p ways. Then p is           (JEE Adv. 2013)

Ans. 5

Solution. Given 8 vectors are

(1, 1, 1), (–1, –1, –1); (–1, 1, 1), (1, –1, –1); (1, –1, 1),
(–1, 1, –1); (1, 1, –1), (–1, –1, 1)
These are 4 diagonals of a cube and their opposites.
For 3 non coplanar vectors first we select 3 groups of diagonals and its opposite in 4C3 ways. Then one vector from each group can be selected in 2 × 2 × 2 ways.

∴ Total ways = 4C3 × 2 × 2× 2 = 32 = 25

∴ p = 5


Q. 6. A pack contains n cards numbered from 1 to n . Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k – 20 =          (JEE Adv. 2013)

Ans. 5

Solution. Let k, k + 1 be removed from pack.

∴ (1 + 2 + 3 + ... + n) – (k + k + 1) = 1224

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


Q. 7. Let Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE be three non-coplanar unit vectors suchthat the angle between every pair of them is π/3. If  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE where p, q and r are scalars, then the value of  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  (JEE Adv. 2014)

Ans. 4

Solution. 

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

Taking its dot product with  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE we get

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

From (1) and (3), p = r Using (2) q = – p

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


Q. 8. Suppose that Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEare three non-coplanar vectors in Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  Let the components of a vector Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE be 4, 3 and 5, respectively. If the components of this vector Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are x, y and z, respectively, then the value of 2x + y + z is         (JEE Adv. 2015)

Ans. 9

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

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

⇒  – x + y – z = 4
x – y – z = 3
x + y + z = 5

Solving above equation  Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ 2x + y + z = 9

The document Integer Answer Type Questions: Vector Algebra and Three Dimensional Geometry | 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

Previous Year Questions with Solutions

,

Extra Questions

,

pdf

,

study material

,

ppt

,

Important questions

,

past year papers

,

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

,

Summary

,

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

,

video lectures

,

Viva Questions

,

Sample Paper

,

Semester Notes

,

practice quizzes

,

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

,

MCQs

,

Exam

,

shortcuts and tricks

,

Objective type Questions

,

Free

,

mock tests for examination

;