MCQ
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
- ✓$90^{\circ}$
- B$0^{\circ}$
- C$60^{\circ}$
- D$45^{\circ}$
✓
Answer
Correct option: A.
$90^{\circ}$
(a)$\begin{aligned}& \cos \theta=\frac{\vec{A} \cdot \vec{B}}{|A||B|}=\frac{(3 \hat{i}+4\hat{j}+5 \hat{k})(3 \hat{i}+4 \hat{j}-5 \hat{k})}{\sqrt{9+16+25} \sqrt{9+16+25}} \\&=\frac{9+16-25}{50}=0 \\& \Rightarrow \cos \theta=0, \therefore \theta=90^{\circ\end{aligned}$
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