Question

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

• A. ${60}^{\circ }$
• B. $0^{\circ }$
• C. ${90}^{\circ }$
• D. None of these

Answer 1

The correct option is C ${90}^{\circ }$

Angle is given as $\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{|A||B|}$

Thus, $\cos \theta =\frac{(3\hat{i}+4\hat{j}+5\hat{k}).(3\hat{i}+4\hat{j}-5\hat{k})}{\sqrt{9+16+25}}=0$

$cos\theta =0$

Thus $\theta ={90}^0$