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

\(\begin{array}{l}1. \ Two \ vectors \ 2\hat{i}+3\hat{j}+8\hat{k} \ and \ 4\hat{j}-4\hat{j}+\alpha\hat{k} \ are \ perpendicular \ to \ each \ other. \ What \ is \ the \ value \ of \ \alpha?\end{array} \)
  1. ยฝ
  2. -ยฝ
  3. 1
  4. -1

Answer: (b) -ยฝ

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

\(\begin{array}{l}4. If \ \vec{A}\ \times \vec{B}=\vec{A}.\vec{B} \ then \ the \ angle \ between \ A \ and \ B \ will \ be\end{array} \)
  1. ฯ€
  2. ฯ€/2
  3. ฯ€/3
  4. ฯ€/4

Answer: (d)ย ฯ€/4

\(\begin{array}{l}5. \ What \ is \ the \ value \ of \ \left | \vec{P} \times \vec{Q}\right | \ if \ \vec{P}=3\hat{i}+\hat{j}+2\hat{k} \ and \ \vec{Q}=2\hat{i}-2\hat{j}+4\hat{k}?\end{array} \)
  1. \(\begin{array}{l}8\sqrt{3}\end{array} \)
  2. \(\begin{array}{l}3\sqrt{8}\end{array} \)
  3. \(\begin{array}{l}4\sqrt{3}\end{array} \)
  4. \(\begin{array}{l}3\sqrt{4}\end{array} \)

Answer: (a)

\(\begin{array}{l}8\sqrt{3}\end{array} \)
\(\begin{array}{l}6. \ If \vec{P}\times\vec{Q}=\vec{R}, \ then \ which \ of \ the \ following \ statements \ is \ true?\end{array} \)
  1. \(\begin{array}{l}\vec{R}\perp \vec{P}\end{array} \)
  2. \(\begin{array}{l}\vec{R}\perp \vec{Q}\end{array} \)
  3. \(\begin{array}{l}\vec{R}\perp (\vec{P}+\vec{Q})\end{array} \)
  4. \(\begin{array}{l}\vec{R}\perp (\vec{P}\times \vec{Q})\end{array} \)

Answer: (d)

\(\begin{array}{l}\vec{R}\perp (\vec{P}\times \vec{Q})\end{array} \)
\(\begin{array}{l}7. \ The \ magnitude \ of \ the \ scalar \ product \ of \ the \ vectors \ \vec{V_1}=2\hat{i}+5\hat{k} \ and \vec{V_2}=3\hat{j}+4\hat{k} \ is\end{array} \)
  1. 20
  2. 36
  3. 24
  4. 34

Answer: (a) 20

\(\begin{array}{l}8. \ Which \ of \ the \ following \ statements \ is \ true \ if \ \vec{P} \ and \ \vec{Q} \ are \ perpendicular \ to \ each \ other?\end{array} \)
  1. \(\begin{array}{l}\vec{P}+\vec{Q}=0\end{array} \)
  2. \(\begin{array}{l}\vec{P}-\vec{Q}=0\end{array} \)
  3. \(\begin{array}{l}\vec{P}\cdot \vec{Q}=0\end{array} \)
  4. \(\begin{array}{l}\vec{P}\times \vec{Q}=0\end{array} \)

Answer: (c)

\(\begin{array}{l}\vec{P}\cdot \vec{Q}=0\end{array} \)
\(\begin{array}{l}9. \ What \ is \ the \ angle \ between \ the \ vectors -2\hat{i}+3\hat{j}+\hat{k} \ and \ \hat{i}+2\hat{j}+-4\hat{k}?\end{array} \)
  1. \(\begin{array}{l}0^{\circ}\end{array} \)
  2. \(\begin{array}{l}25^{\circ}\end{array} \)
  3. \(\begin{array}{l}90^{\circ}\end{array} \)
  4. \(\begin{array}{l}180^{\circ}\end{array} \)

Answer: (c)

\(\begin{array}{l}90^{\circ}\end{array} \)
\(\begin{array}{l}10. \ A \ force \ \vec{F}=5\hat{i}+6\hat{i}+4\hat{k} \ acts \ on \ a \ body \ and \ displaces \ it \ by \ \vec{S}=6\hat{i}-5\hat{k}. \ What \ is \ the \ work \ done \ by \ the \ force?\end{array} \)
  1. 5 Units
  2. 10 Units
  3. 15 Units
  4. 20 Units

Answer: (b) 10 Units

\(\begin{array}{l}11. \ What \ is \ the \ area \ of \ the \ parallelogram \ which \ represented \ by \ vectors \ \vec{P}=2\hat{i}+3\hat{j} \ and \ \vec{Q}={i}+4\hat{j}?\end{array} \)
  1. 5 Units
  2. 10 Units
  3. 15 Units
  4. 20 Units

Answer: (a) 5 Units

\(\begin{array}{l}12. \ What \ is \ the \ angle \ between \ vectorsย \ \vec{A}\times \vec{B}\ andย \ \vec{B}\times \ \vec{A}?\end{array} \)
  1. ฯ€
  2. 00
  3. ฯ€/2
  4. ฯ€/4

Answer: (a)

\(\begin{array}{l}13. \ The \ angle \ between \ \vec{A}+\vec{B} \ andย \ \vec{A}\times \vec{B} \ is\end{array} \)
  1. ฯ€
  2. ฯ€/2
  3. ฯ€/4
  4. 0

Answer: (b) ฯ€/2

\(\begin{array}{l}14. \ The \ vectors \ \vec{a}, \ \vec{b} \ and \ \vec{c} \ satisfy \ the \ relation \ \vec{a}\cdot \vec{b}=0 \ and \ \vec{a}\cdot \vec{c}=0. \ The \ vector \ \vec{a} \ is \ parallel \ to\end{array} \)
  1. \(\begin{array}{l}\vec{b}\cdot \vec{c}\end{array} \)
  2. \(\begin{array}{l}\vec{b}\times \vec{c}\end{array} \)
  3. \(\begin{array}{l}\vec{b}\end{array} \)
  4. \(\begin{array}{l}\vec{c}\end{array} \)

Answer: (b)

\(\begin{array}{l}\vec{b}\times \vec{c}\end{array} \)

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