 # 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) $\vec{b}\times \vec{c}$