Check the below NCERT MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Vector Algebra Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 The length of longer diagronai of the parallelogram constructed on 5a + 2b and a – 3b. If it is given that

|a| = 2√2, |b| = 3 and angle between a and b is π/4, is

(a) 15

(b) √113

(c) √593

(d) √369

## Q.2 Which of the following represents equal vectors?

(a) a, c

(b) b, d

(c) b, c

(d) m, d

## Q.3 Which of the following represents collinear but not equal vectors?

(a) a, c

(b) b, d

(c) b, m

(d) Both (a) and (b)

## Q.4 The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is

(a) √3

(b) 1 – √3

(c) 1 + √3

(d) -√3

## Q.5 Which of the following represents coinitial vector?

(a) c, d

(b) m, b

(c) b, d

(d) Both (a) and (b)

## Q.6 If a + b + c = 0, then a × b =

(a) c × a

(b) b × c

(c) 0

(d) Both (a) and (b)

## Q.7 The points with position vectors (2. 6), (1, 2) and (a, 10) are collinear if the of a is

(a) -8

(b) 4

(c) 3

(d) 12

## Q.8 If a, b, c are three non-coplanar vectors, then (a + b + c).[(a + b) × (a + c)] is

(a) 0

(b) 2[abc]

(c) -[abc]

(d) [abc]

## Q.9 If u, v and w are three non-coplanar vectors, then (u + v – w).[(u – v) × (v – w)] equals

(a) 0

(b) u.v × w

(c) u.w × v

(d) 3u.v × w

## Q.10 If a, b, c are unit vectors, then |a – b| + |b – c| + |c – a| does not exceed

(a) 4

(b) 9

(c) 8

(d) 6

## Q.11 |a × b|² + |a.b|² = 144 and |a| = 4, then |b| is equal to

(a) 12

(b) 3

(c) 8

(d) 4

## Q.12 If |a × b| = 4 and |a.b| = 2, then |a|² |b|² is equal to

(a) 2

(b) 6

(c) 8

(d) 20

## Q.13 If |a|= 5, |b|= 13 and |a × b|= 25, find a.b

(a) ±10

(b) ±40

(c) ±60

(d) ±25

## Q.14 The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is

(a) √3

(b) 1 – √3

(c) 1 + √3

(d) -√3

## Q.15 The distance of the point (- 3, 4, 5) from the origin

(a) 50

(b) 5√2

(c) 6

(d) None of these

## Q.16 If a, b, c are unit vectors such that a + b + c = 0, then the value of a.b + b.c + c.a is

(a) 1

(b) 3

(c) −3/2

(d) None of these

## Q.17 The ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1, -5, 7) is

(a) 5 : 3

(b) 3 : 2

(c) 2 : 1

(d) 1 : 3

## Q.18 If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is

(a) [0, 8]

(b) [-12, 8]

(c) [0, 12]

(d) [8, 12]

## Q.19 Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a

is

(a) 47

(b) 25

(c) 50

(d) -25

## Q.20 a, b, c are three vectors, such that a + b + c = 0, |a|= 1, |b|= 2, |c|= 3, then a.b + b.c + c is equal to

(a) 0

(b) -7

(c) 7

(d) 1

## Q.21 The vectors (x, x + 1, x + 2), (x + 3, x + 4, x + 5) and (x + 6, x + 7, x + 8) are coplanar for

(a) all values of x

(b) x < 0

(c) x ≤ 0

(d) None of these