Multiplication of Vectors MCQs for NEET 2023

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. T w o v e c t o r s 2 \hat{i} + 3 \hat{j} + 8 \hat{k} a n d 4 \hat{j} - 4 \hat{j} + α \hat{k} a r e p e r p e n d i c u l a r t o e a c h o t h e r . W h a t i s t h e v a l u e o f α ? \end{array}

½
-½
1
-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?

100 J
150 J
200 J
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
2
3
4

Answer: (a) 1

\begin{array}{l} 4. I f \vec{A} \times \vec{B} = \vec{A} . \vec{B} t h e n t h e a n g l e b e t w e e n A a n d B w i l l b e \end{array}

π
π/2
π/3
π/4

Answer: (d) π/4

\begin{array}{l} 5. W h a t i s t h e v a l u e o f | \vec{P} \times \vec{Q} | i f \vec{P} = 3 \hat{i} + \hat{j} + 2 \hat{k} a n d \vec{Q} = 2 \hat{i} - 2 \hat{j} + 4 \hat{k} ? \end{array}

$\begin{array}{l} 8 \sqrt{3} \end{array}$
$\begin{array}{l} 3 \sqrt{8} \end{array}$
$\begin{array}{l} 4 \sqrt{3} \end{array}$
$\begin{array}{l} 3 \sqrt{4} \end{array}$

Answer: (a)

\begin{array}{l} 8 \sqrt{3} \end{array}

\begin{array}{l} 6. I f \vec{P} \times \vec{Q} = \vec{R}, t h e n w h i c h o f t h e f o l l o w i n g s t a t e m e n t s i s t r u e ? \end{array}

$\begin{array}{l} \vec{R} ⊥ \vec{P} \end{array}$
$\begin{array}{l} \vec{R} ⊥ \vec{Q} \end{array}$
$\begin{array}{l} \vec{R} ⊥ (\vec{P} + \vec{Q}) \end{array}$
$\begin{array}{l} \vec{R} ⊥ (\vec{P} \times \vec{Q}) \end{array}$

Answer: (d)

\begin{array}{l} \vec{R} ⊥ (\vec{P} \times \vec{Q}) \end{array}

\begin{array}{l} 7. T h e m a g n i t u d e o f t h e s c a l a r p r o d u c t o f t h e v e c t o r s \vec{V_{1}} = 2 \hat{i} + 5 \hat{k} a n d \vec{V_{2}} = 3 \hat{j} + 4 \hat{k} i s \end{array}

20
36
24
34

Answer: (a) 20

\begin{array}{l} 8. W h i c h o f t h e f o l l o w i n g s t a t e m e n t s i s t r u e i f \vec{P} a n d \vec{Q} a r e p e r p e n d i c u l a r t o e a c h o t h e r ? \end{array}

$\begin{array}{l} \vec{P} + \vec{Q} = 0 \end{array}$
$\begin{array}{l} \vec{P} - \vec{Q} = 0 \end{array}$
$\begin{array}{l} \vec{P} \cdot \vec{Q} = 0 \end{array}$
$\begin{array}{l} \vec{P} \times \vec{Q} = 0 \end{array}$

Answer: (c)

\begin{array}{l} \vec{P} \cdot \vec{Q} = 0 \end{array}

\begin{array}{l} 9. W h a t i s t h e a n g l e b e t w e e n t h e v e c t o r s - 2 \hat{i} + 3 \hat{j} + \hat{k} a n d \hat{i} + 2 \hat{j} + - 4 \hat{k} ? \end{array}

$\begin{array}{l} 0^{\circ} \end{array}$
$\begin{array}{l} 25^{\circ} \end{array}$
$\begin{array}{l} 90^{\circ} \end{array}$
$\begin{array}{l} 180^{\circ} \end{array}$

Answer: (c)

\begin{array}{l} 90^{\circ} \end{array}

\begin{array}{l} 10. A f o r c e \vec{F} = 5 \hat{i} + 6 \hat{i} + 4 \hat{k} a c t s o n a b o d y a n d d i s p l a c e s i t b y \vec{S} = 6 \hat{i} - 5 \hat{k} . W h a t i s t h e w o r k d o n e b y t h e f o r c e ? \end{array}

5 Units
10 Units
15 Units
20 Units

Answer: (b) 10 Units

\begin{array}{l} 11. W h a t i s t h e a r e a o f t h e p a r a l l e l o g r a m w h i c h r e p r e s e n t e d b y v e c t o r s \vec{P} = 2 \hat{i} + 3 \hat{j} a n d \vec{Q} = i + 4 \hat{j} ? \end{array}

5 Units
10 Units
15 Units
20 Units

Answer: (a) 5 Units

\begin{array}{l} 12. W h a t i s t h e a n g l e b e t w e e n v e c t o r s \vec{A} \times \vec{B} a n d \vec{B} \times \vec{A} ? \end{array}

π
0⁰
π/2
π/4

Answer: (a)

\begin{array}{l} 13. T h e a n g l e b e t w e e n \vec{A} + \vec{B} a n d \vec{A} \times \vec{B} i s \end{array}

π
π/2
π/4
0

Answer: (b) π/2

\begin{array}{l} 14. T h e v e c t o r s \vec{a}, \vec{b} a n d \vec{c} s a t i s f y t h e r e l a t i o n \vec{a} \cdot \vec{b} = 0 a n d \vec{a} \cdot \vec{c} = 0. T h e v e c t o r \vec{a} i s p a r a l l e l t o \end{array}

$\begin{array}{l} \vec{b} \cdot \vec{c} \end{array}$
$\begin{array}{l} \vec{b} \times \vec{c} \end{array}$
$\begin{array}{l} \vec{b} \end{array}$
$\begin{array}{l} \vec{c} \end{array}$

Answer: (b)

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

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Fizza noor

December 22, 2020 at 5:16 pm

I love this website. This website is a good way for learning and to ready MCQs for any topic.

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