Vector Algebra MCQ for ISC Class-12 Maths

Vector Algebra MCQ for ISC Class-12 Maths .These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.

ISC Class-12 Maths , Vector Algebra MCQ Type Questions

Board	ISC
Class	12th (XII)
Subject	Maths
Ch-Name	Vector Algebra
Syllabus	on bifurcated syllabus (after reduction)
Bifurcated pattern	Semester-1
Session	2021-22
Topic	MCQ / Objective Type Question

Vector Algebra MCQ Type Questions for ISC Class-12 Maths

Question 1: 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

(d) 3u.v × w

Answer: (b) u.v × w

Question 2: If a, b, c are unit vectors, then |a – b| + |b – c| + |c – a| does not exceed

(a) 4

(b) 9

(d) 6

Answer: (b) 9

Question 3: Find the magnitude of vector 3𝑖̂ +2𝑗̂ +12𝑘̂ .

(a) √157

(b) 4√11

(d) 9√3

Answer: (a) √157

Question 4: The vectors AB = 3𝑖̂ +4𝑘̂ and AC = 𝐴𝐶=5𝑖̂ −2𝑗̂ +4𝑘̂ are the side of a ΔABC. The length of the median through A is

(a) √18

(b) √72

(d) √288

Answer: (c) √33

Question 5: The area of parallelogram whose adjacent sides are 𝑖̂ −2𝑗̂ +3𝑘̂ and 2𝑖̂ +𝑗̂ −4𝑘̂ is

(a) 10√6

(b) 5√6

(d) 5√3

Answer: (b) 5√6

Question 6: |a × b|² + |a.b|² = 144 and |a| = 4, then |b| is equal to

(a) 12

(b) 3

(d) 4

Answer: (b) 3

Question 7: Find the value of λ so that the vectors 2𝑖−4𝑗̂ +𝑘̂ and 4𝑖−8𝑗̂ +𝜆𝑘̂ are parallel.

(a) -1

(b) 3

(d) 2

Answer: (d) 2

Question 8: Find the value of λ so that the vectors 2𝑖̂ −4𝑗̂ +𝑘̂ and 4𝑖̂ −8𝑗̂ +𝜆𝑘̂ are perpendicular.

(a) -15

(b) 10

(d) 20

Answer: (c) -40

Question 9: 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

(d) √369

Answer: (c) √593

Question 10: The number of vectors of unit length perpendicular to the vectors a = 2𝑖̂ +𝑗̂ +2𝑘̂ and b = 𝑗̂ +𝑘̂ is

(a) one

(b) two

(d) infinite

Answer: (b) two

Question 11: If |a|= 5, |b|= 13 and |a × b|= 25, find a.b

(a) ±10

(b) ±40

(d) ±25

Answer: (c) ±60

Question 12: If O is origin and C is the mid point of A(2, -1) and B(-4, 3), then the value of OC is

(a) 𝑖̂ +𝑗̂

(b) 𝑖̂ −𝑗̂

(d) −𝑖̂ −𝑗̂

Answer: (c) −𝑖̂ +𝑗̂

Question 13: If a is perpendicular to b and c, |a| = 2, |b| = 3, |c| = 4 and the angle between b and c is 2𝜋/3, |abc| is equal to

(a) 4√3

(b) 6√3

(d) 18√3

Answer: (c) 12√3

Question 14: If the angle between 𝑖̂ +𝑘̂ and 𝑖̂ +𝑗̂ +𝑎𝑘̂ is 𝜋/3, then the value of a is

(a) 0 or 2

(b) -4 or 0

(d) 2 or -2

Answer: (b) -4 or 0

Question 15: The vectors 𝜆𝑖̂ +𝑗̂ +2𝑘̂ ,𝑖̂ +𝜆𝑗̂ −𝑘̂ and 2𝑖̂ −𝑗̂ +𝜆𝑘̂ are coplanar if

(a) λ = -2

(b) λ = 0

(d) λ = -1

Answer: (a) λ = -2

Question 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

(d) None of these

Answer: (c) −3/2

Question 17: If |a × b| = 4 and |a.b| = 2, then |a|²|b|² is equal to

(a) 2

(b) 6

(d) 20

Answer: (d) 20

Question 18: If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is

(a) [0, 8]

(b) [-12, 8]

(d) [8, 12]

Answer: (c) [0, 12]

Question 19: 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

(d) -√3

Answer: (a) √3

Question 20: 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

(d) -25

Answer: (d) -25

Question 21: The distance of the point (- 3, 4, 5) from the origin

(a) 50

(b) 5√2

(d) None of these

Answer: (b) 5√2

Question 22: The value of λ for which the vectors 3𝑖̂ −6𝑗̂ +𝑘̂ and 2𝑖̂ −4𝑗̂ +𝜆𝑘̂ are parallel is

(a) 2/3

(b) 3/2

(d) 2/5

Answer: (a) 2/3

Question 23: 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

(d) 1 : 3

Answer: (a) 5 : 3

Question 24: If AB × AC = 2𝑖̂ −4𝑗̂ +4𝑘̂ , then the are of ΔABC is

(a) 3 sq. units

(b) 4 sq. units

(d) 9 sq. units

Answer: (a) 3 sq. units

Question 25: The vectors 3𝑖̂ +5𝑗̂ +2𝑘̂ ,2𝑖̂ −3𝑗̂ −5𝑘̂ and 5𝑖̂ +2𝑗̂ −3𝑘̂ form the sides of

(a) Isosceles triangle

(b) Right triangle

(d) Equilaterala triangle

Answer: (d) Equilaterala triangle

Question 26: If a + b + c = 0, then a × b =

(a) c × a

(b) b × c

(d) Both (a) and (b)

Answer: (d) Both (a) and (b)

Question 27: If a, b, c are three non-coplanar vectors, then (a + b + c).[(a + b) × (a + c)] is

(a) 0

(b) 2[abc]

(d) [abc]

Answer: (c) -[abc]

Question 28: The dot product of a vector with the vectors 𝑖̂ +𝑗̂ −3𝑘̂ ,𝑖̂ +3𝑗̂ −2𝑘̂ and 2𝑖̂ +𝑗̂ +4𝑘̂ are 0, 5 and 8 respectively. Find the vector.

(a) 𝑖̂ +2𝑗̂ +𝑘̂

(b) −𝑖̂ +3𝑗̂ −2𝑘̂

(d) 𝑖̂ −3𝑗̂ −3𝑘̂

Answer: (a) 𝑖̂ +2𝑗̂ +𝑘

Question 29: If |a| = |b| = 1 and |a + b| = √3, then the value of (3a – 4b).(2a + 5b) is

(a) -21

(b) −21/2

(d) 21/2

Answer: (b) −21/2

Question 30: The points with position vectors (2. 6), (1, 2) and (a, 10) are collinear if the of a is

(a) -8

(b) 4

(d) 12

Answer: (c) 3

Question 31: Three points (2, -1, 3), (3, – 5, 1) and (-1, 11, 9) are

(a) Non-collinear

(b) Non-coplanar

(d) None of these

Answer: (c) Collinear

Question 32: 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

(d) None of these

Answer: (a) all values of x

Question 33: 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

(d) -√3

Answer: (a) √3

Question 34: If a, b, c are three mutually perpendicular vectors of equal magnitude, find the angle between a and a + b + c.

(a) cos−¹(1/√3)

(b) cos−¹(1/2√2)

(d) cos−¹(1/2√3)

Answer: (a) cos−1(1/√3)

Question 35: The vectors from origin to the points A and B are a = 2𝑖̂ −3𝑗̂ +2𝑘̂ and b = 2𝑖̂ +3𝑗̂ +𝑘̂ , respectively then the area of triangle OAB is