Motion in a Plane - Result Question 11
13. The angle between the two vectors $\vec{A}=3 \hat{i}+4 \hat{j}+5 \hat{k}$ and $\vec{B}=3 \hat{i}+4 \hat{j}-5 \hat{k}$ will be
(a) zero
(b) $45^{\circ}$
(c) $90^{\circ}$
(d) $180^{\circ}$
[2001, 1994]
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Answer:
Correct Answer: 13. (c)
Solution:
- (c) $\vec{A}=3 \hat{i}+4 \hat{j}+5 \hat{k}, \vec{B}=3 \hat{i}+4 \hat{j}-5 \hat{k}$
$\vec{A} \cdot \vec{B}=(3 \hat{i}+4 \hat{j}+5 \hat{k}) \cdot(3 \hat{i}+4 \hat{j}-5 \hat{k})$
$|\vec{A}||\vec{B}| \cos \theta=9+16-25=0$
$|\vec{A}| \neq 0,|\vec{B}| \neq 0$, hence, $\cos \theta=0, \theta=90^{\circ}$
