# Class 12 Mathematics Chapter 10 Vector Algebra MCQ Questions with Answer

Class 12 Vector Algebra MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Vector Algebra Class 12, which will help them all through their board test.

## Class 12 Vector Algebra MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 10 Vector Algebra. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Vector Algebra Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Vector Algebra MCQ with answers given below.

Question 1. 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]

C

Question 2. The area of a triangle formed by vertices O, A, B where OA = î + 2ĵ + 3k̂OA and OB= –3î – 2ĵ + k̂
(a) 3√5 sq. units
(b) 5√5 sq. units
(c) 6 5 sq. units
(d) 4 sq. units

A

Question 3. The vectors 3î – ĵ + 2k̂, 2î + ĵ + 3k̂ and iî + mĵ – k̂ are coplanar if
(a) –2
(b) 0
(c) 2
(d) Any real number

A

Question 4. The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4) respectively is
(a) î – 12ĵ + 4k̂
(b) 5î – 2ĵ + 4k̂
(c)-5î + 2ĵ + 4k̂
(d) î –  ĵ +  k̂

C

Question 5. The angle between two vectors a🠖 and b🠖 with magnitudes 3 and 4 respectively and a🠖. b🠖 = 2√3 is
(a) π/6
(b) π/3
(c) π/2
(d) 5π/2

B

Question 6. The position vector of the point which divides the join of point 2a🠖– 3b🠖and a🠖 + b🠖 in the ratio 3 : 1 is
(a) 3a🠖– 3b🠖/2
(b) 7a🠖– 8b🠖/4
(c) 3a🠖/4
(d) 5a🠖/4

D

Question 7. The position vector of the point which divides the join of points with position vectors a🠖+ b🠖and 2a🠖 – b🠖 in the ratio 1 : 2 is
(a) 3a🠖+ 2b🠖 /3
(b) a🠖
(c) 5a🠖+ b🠖 /3
(d) 4a🠖+ b🠖 /3

D

Question 8. Find the value of λ such that the vectors a🠖 = 2î + mĵ + k̂ and b🠖 = î + 2ĵ + 3k̂ are orthogonal
(a) 0
(b) 1
(c) 3/2
(d) -5/2

D

Question 9. The value of λ for which the vectors 3î – 6ĵ + k̂ and 2î – 4ĵ + mk̂ are parallel is
(a) 2/3
(b) 3/2
(c) 5/2
(d) 2/5

A

Question 10. If a🠖, b🠖 and c🠖 are three vectors such that a🠖 + b🠖 + c🠖 = 0 and a🠖 = 2, b🠖 = 3, c🠖= 5, then value
of a🠖. b🠖 +b🠖.c🠖+ c🠖. a🠖 is
(a) 0
(b) 1
(c) – 19
(d) 38

C

Question 11. For any vector a🠖, the value of (a🠖 × î)2+(a🠖 × ĵ)2+(a🠖 × k̂)2 is equal to
(a) a🠖2
(b) 3a🠖2
(c) 4a🠖2
(d) 2a🠖2

D

Question 12. The vector 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
(a) 340
(b) 25
(c) 229
(d) (1/2)√229

D

Question 13. The vector λî + ĵ + 2k̂, î + λĵ  – k̂ and 2î – ĵ + λk̂ are coplanar if
(a) λ = –2
(b) λ = 0
(c) λ = 1
(d) λ = – 1

A

Question 14. The value of î. (ĵ×k̂) + ĵ. (î×k̂) + k̂. (î×ĵ) is
(a) 0
(b) – 1
(c) 1
(d) 3

B

Question 15. If |a🠖| = 10, |b🠖| = 2 and a🠖 . b🠖 = 12, then value of a🠖 × b🠖 is
(a) 5
(b) 10
(c) 14
(d) 16

D

Question 16. The number of vectors of unit length perpendicular to the vectors a🠖 = 2î + ĵ + 2k̂ and b🠖 = ĵ + k̂ is
(a) one
(b) two
(c) three
(d) infinite

B

Question 17. 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

C

Question 18. The magnitude of the vector 6î + 2ĵ + 3k̂ is
(a) 5
(b) 7
(c) 12
(d) 1

B

Question 19. The vector of the direction of the vector î – 2ĵ + 2k̂ that has magnitude 9 is
(a) î – 2ĵ + 2k̂
(b) î – 2ĵ + 2k̂/3
(c) 3(î – 2ĵ + 2k̂)
(d) 9(î – 2ĵ + 2k̂)

C

Question 20. Let a🠖 and b🠖 be two unit vectors and θ is the angle between them. Then a🠖 + b🠖is unit vector if q is
(a) π/4
(b) π/3
(c) π/2
(d) 2π/3

D

Question 21. The value of p for which p(î + ĵ + k̂) is a unit vector is
(a) 0
(b) 1/√3
(c) 1
(d) 3

B

Question 22. Let a🠖 = î – 2ĵ + 3k̂. If b is a vector such that a🠖. b🠖 |b🠖|2 and |a🠖 – b🠖 = √7  then |b🠖| equals
(a) 7
(b) 14
(c) 7
(d) 21

C

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Vector Algebra Class 12 MCQ are ready by the subject specialists themselves.

## Fill in the blanks

Question 1. The value of l for which the vectors 2î – mĵ + k̂ and it + 2ĵ – k̂ are orthogonal is ____________.

λ=1/2

Question 2. If a🠖 = 3î – 2ĵ + 2k̂, b🠖 = 6î + 4ĵ – 2k̂ and c = –3it – 2ĵ + 4k̂. Then a🠖 . _b🠖 # c i is equal to _________.

72

Question 3. The area of the parallelogram whose diagonals are 2î and –3k̂ is ___________ square units.

3 sq. units

Question 4. The sine of the angle between vectors a🠖 = 2î – 6ĵ – 3k̂ and b🠖 = 4î + 3ĵ – k̂ is equal to _________.

5/√26

Question 5. If |a🠖 b🠖|2 + |a🠖.b🠖|2 144 and |a🠖| 4 , then |b🠖| is equal to _____________ .

3

Question 6. The vectors a🠖 = 3î – 2ĵ + 2k̂ and b🠖 = –î –2k̂ are the adjacent sides of a parallelogram. The acute angle between its diagonals is _____________

π/4

Question 7. The projection of the vector î – ĵ on the vector î + ĵ is _____________ .

0

Question 8. The area of the triangle whose adjacent sides are a🠖 = î + 4ĵ – k̂ and b = î + ĵ + 2k̂ is _____________ sq. units.

3/2√11 Sq. units.

Question 9. If a is a non-zero vector, then _(a .î)î +`(a . ĵ)ĵ +_(a . k̂)k̂ equals _____________ .

a🠖

Question 10. If |a🠖| = 1 and a🠖 x î = ĵ , then angle between a🠖 and î is _____________ .

π/2

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