300+ TOP MCQs on Multiplication of Vectors and Answers

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MCQs on Multiplication of Vectors :

1. Two vectors (2 hat{i}+3 hat{j}+8 hat{k}) and (4 hat{j}-4 hat{j}+alpha hat{k}) are perpendicular to each other. What is the value of α?
(A) ½
(B) -½
(C) 1
(D) -1

Answer

Answer: (B) -½

2. A force of 50 N acts on a body and displaces it through a distance of 10 meters in a direction making an angle of 60⁰ with the force. What is the work done by the force?
(A) 100 J
(B) 150 J
(C) 200 J
(D) 250 J

Answer

Answer: (D) 250 J

3. If the sum of two vectors is perpendicular to the difference between them. The ratio of their magnitude will be
(A) 1
(B) 2
(C) 3
(D) 4

Answer

Answer: (A) 1

4. If (vec{A} times vec{B}=vec{A} cdot vec{B})  then the angle between A and B will be
(A) π
(B) π/2
(C) π/3
(D) π/4

Answer

Answer: (D) π/4

5. What is the value of (|vec{P} times vec{Q}| text { if } vec{P}=3 hat{i}+hat{j}+2 hat{k} text { and } vec{Q}=2 hat{i}-2 hat{j}+4 hat{k} )?
(A) 8√3
(B) 3√8
(C) 4√3
(D) 3√4

Answer

Answer: (A) 8√3

6. If (vec{P} times vec{Q}=vec{R}), then which of the following statements is true?

Answer

Answer: (D) (vec{R} perp(vec{P} times vec{Q}))

7. The magnitude of the scalar product of the vectors (overrightarrow{V_{1}}=2 hat{i}+5 hat{k}) and (overrightarrow{V_{1}}=2 hat{i}+5 hat{k}) is
(A) 20
(B) 36
(C) 24
(D) 34

Answer

Answer: (A) 20

8. Which of the following statements is true if (vec{P})  and (vec{Q}) are perpendicular to each other?

Answer

Answer: (C) (vec{P} cdot vec{Q}=0)

9. What is the angle between the vectors (-2 hat{i}+3 hat{j}+hat{k}) and (hat{i}+2 hat{j}+-4 hat{k})?
(A) 0°
(B) 25°
(C) 90°
(D) 180°

Answer

Answer: (C) 90°

10. A force (vec{F}=5 hat{i}+6 hat{i}+4 hat{k}) acts on a body and displaces it by (vec{S}=6 hat{i}-5 hat{imath}). What is the work done by the force?
(A) 5 Units
(B) 10 Units
(C) 15 Units
(D) 20 Units

Answer

Answer: (B) 10 Units

11. What is the area of the parallelogram which represented by vectors (vec{P}=2 hat{i}+3 hat{j}) and (vec{Q}=i+4 hat{j})?
(A) 5 Units
(B) 10 Units
(C) 15 Units
(D) 20 Units

Answer

Answer: (A) 5 Units

12. What is the angle between vectors (vec{A} times vec{B}) and (vec{B} times vec{A})?
(A) π
(B) 0⁰
(C) π/2
(D) π/4

Answer

Answer: (A) π

13. The angle between (vec{A}+vec{B}) and (vec{A} times vec{B}) is
(A) π
(B) π/2
(C) π/4
(D) 0

Answer

Answer: (B) π/2

14. The vectors (vec{a}), (vec{b}) and (vec{c}) satisfy the relation (vec{a} cdot vec{b}=0) and (vec{a} cdot vec{c}=0). The vector (vec{a}) is parallel to

Answer

Answer: (B)  (vec{b} times vec{c})