Multiplication of Vectors MCQs

 The angle between two vectors plays an important role when the two vectors are multiplied. Following are the two ways through a vector multiplication can be carried out:

• Multiplication of a Vector by a scalar
• Multiplication of a vector by a vector

The multiplication of a vector by a vector can be carried out in two ways and they are termed as:

• Dot Product
• Cross Product

The result of a dot product of two vectors is a scalar quantity. The result of the cross product of two vectors is a vector quantity.

Question and Answer

1. Two vectors 2i^+3j^+8k^ and 4j^−4j^+αk^ are perpendicular to each other. What is the value of α?

1. ½
2. -½
3. 1
4. -1

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?

1. 100 J
2. 150 J
3. 200 J
4. 250 J

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

1. 1
2. 2
3. 3
4. 4

Answer: (a) 1

4. If A⃗ ×B⃗ =A⃗ .B⃗  then the angle between A and B will be

1. π
2. π/2
3. π/3
4. π/4

Answer: (d) π/4

5. What is the value of ∣∣P⃗ ×Q⃗ ∣∣ if P⃗ =3i^+j^+2k^ and Q⃗ =2i^−2j^+4k^?

1. 83–√
2. 38–√
3. 43–√
4. 34–√

Answer: (a) 83–√

6. If P⃗ ×Q⃗ =R⃗ , then which of the following statements is true?

1. R⃗ ⊥P⃗ 
2. R⃗ ⊥Q⃗ 
3. R⃗ ⊥(P⃗ +Q⃗ )
4. R⃗ ⊥(P⃗ ×Q⃗ )

Answer: (d) R⃗ ⊥(P⃗ ×Q⃗ )

7. The magnitude of the scalar product of the vectors V1→=2i^+5k^ and V2→=3j^+4k^ is

1. 20
2. 36
3. 24
4. 34

Answer: (a) 20

8. Which of the following statements is true if P⃗  and Q⃗  are perpendicular to each other?

1. P⃗ +Q⃗ =0
2. P⃗ −Q⃗ =0
3. P⃗ ⋅Q⃗ =0
4. P⃗ ×Q⃗ =0

Answer: (c) P⃗ ⋅Q⃗ =0

9. What is the angle between the vectors −2i^+3j^+k^ and i^+2j^+−4k^?

1. 0∘
2. 25∘
3. 90∘
4. 180∘

Answer: (c) 90∘

10. A force F⃗ =5i^+6i^+4k^ acts on a body and displaces it by S⃗ =6i^−5k^. What is the work done by the force?

1. 5 Units
2. 10 Units
3. 15 Units
4. 20 Units

Answer: (b) 10 Units

11. What is the area of the parallelogram which represented by vectors P⃗ =2i^+3j^ and Q⃗ =i+4j^?

1. 5 Units
2. 10 Units
3. 15 Units
4. 20 Units

Answer: (a) 5 Units

12. What is the angle between vectors A⃗ ×B⃗  and B⃗ ×A⃗ ?

1. π
2. 00
3. π/2
4. π/4

Answer: (a)

13. The angle between A⃗ +B⃗  and A⃗ ×B⃗  is

1. π
2. π/2
3. π/4
4. 0

Answer: (b) π/2

14. The vectors a⃗ , b⃗  and c⃗  satisfy the relation a⃗ ⋅b⃗ =0 and a⃗ ⋅c⃗ =0. The vector a⃗  is parallel to

1. b⃗ ⋅c⃗ 
2. b⃗ ×c⃗ 
3. b⃗ 
4. c⃗ 

Answer: (b) b⃗ ×c⃗