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.

Question and Answer

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. -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 \(\vec{A}\times \vec{B}=\vec{A}.\vec{B}\) then the angle between A and B will be

1. π
2. π/2
3. π/3
4. π/4

Answer: (d) 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

Answer: (a) 20

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

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 \(\vec{Q}={i}+4\hat{j}\)?

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

Answer: (a) 5 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

Answer: (a)

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

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

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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