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. 1
  3. -1

Answer: (b)

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

  1. p
  2. p/2
  3. p/3
  4. p/4

Answer: (a) 1

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. 26
  2. 36
  3. 24
  4. 34

Answer: (a) 26

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. p
  2. 00
  3. π/2
  4. π/4

Answer: (a) p

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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