Question

The angle between the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k}$ and $\overrightarrow{B}=3\hat{i}+4\hat{j}-5\hat{k}$ will be

• A. ${90}^{\circ }$
• B. $0^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A

${90}^{\circ }$

$cos\theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{|A||B|}=\frac{(3\hat{i}+4\hat{j}+5\hat{k})(3\hat{i}+4\hat{j}-5\hat{k})}{\sqrt{9+16+25}\sqrt{9+16+25}}$
$=\frac{9+16-25}{50}=0$
$\Rightarrow cos\theta =0,\therefore \theta ={90}^{\circ }$.