 # Multiplication of Vectors MCQs for NEET

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.

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 $$\alpha$$?

1. ½
2. 1
3. -1

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

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

4. If $$\vec{A}\times \vec{B}=\vec{A}.\vec{B}$$ then the angle between A and B will be

1. π
2. π/2
3. π/3
4. π/4

5. What is the value of $$\left | \vec{P} \times \vec{Q}\right |$$ if $$\vec{P}=3\hat{i}+\hat{j}+2\hat{k}$$ and $$\vec{Q}=2\hat{i}-2\hat{j}+4\hat{k}$$?

1. $$8\sqrt{3}$$
2. $$3\sqrt{8}$$
3. $$4\sqrt{3}$$
4. $$3\sqrt{4}$$

Answer: (a) $$8\sqrt{3}$$

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

1. $$\vec{R}\perp \vec{P}$$
2. $$\vec{R}\perp \vec{Q}$$
3. $$\vec{R}\perp (\vec{P}+\vec{Q})$$
4. $$\vec{R}\perp (\vec{P}\times \vec{Q})$$

Answer: (d) $$\vec{R}\perp (\vec{P}\times \vec{Q})$$

7. The magnitude of the scalar product of the vectors $$\vec{V_1}=2\hat{i}+5\hat{k}$$ and $$\vec{V_2}=3\hat{j}+4\hat{k}$$ is

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

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

1. $$\vec{P}+\vec{Q}=0$$
2. $$\vec{P}-\vec{Q}=0$$
3. $$\vec{P}\cdot \vec{Q}=0$$
4. $$\vec{P}\times \vec{Q}=0$$

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 $$\hat{i}+2\hat{j}+-4\hat{k}$$?

1. $$0^{\circ}$$
2. $$25^{\circ}$$
3. $$90^{\circ}$$
4. $$180^{\circ}$$

Answer: (c) $$90^{\circ}$$

10. A force $$\vec{F}=5\hat{i}+6\hat{i}+4\hat{k}$$ acts on a body and displaces it by $$\vec{S}=6\hat{i}-5\hat{k}$$. What is the work done by the force?

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

11. What is the area of the parallelogram which represented by vectors $$\vec{P}=2\hat{i}+3\hat{j}$$ and $$\vec{Q}={i}+4\hat{j}$$?

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

12. What is the angle between vectors $$\vec{A}\times \vec{B}$$ and $$\vec{B}\times \vec{A}$$?

1. π
2. 00
3. π/2
4. π/4

13. The angle between $$\vec{A}+\vec{B}$$ and $$\vec{A}\times \vec{B}$$ is

1. π
2. π/2
3. π/4
4. 0

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

1. $$\vec{b}\cdot \vec{c}$$
2. $$\vec{b}\times \vec{c}$$
3. $$\vec{b}$$
4. $$\vec{c}$$

Answer: (b) $$\vec{b}\times \vec{c}$$

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#### 1 Comment

1. Fizza noor

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