Motion in a Plane - Result Question 11

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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

======= ####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

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/motion-in-a-plane/motion-in-a-plane—result-question-11.md (a) zero

(b) $45^{\circ}$

(c) $90^{\circ}$

(d) $180^{\circ}$

[2001, 1994]

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Answer:

Correct Answer: 13. (c)

Solution:

  1. (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, $\cos \theta=0, \theta=90^{\circ}$