Question

The angle between lines $\frac{x-2}{2}=\frac{y-3}{-2}=\frac{z-5}{1}$ and $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-5}{2}$ is_________.

• A. ${30}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Vector parallel to first line is $2\hat{i}-2\hat{j}+\hat{k}$

Vector parallel to second line is $\hat{i}+2\hat{j}+2\hat{k}$

So cosine of angle between them is $|\frac{(2\hat{i}-2\hat{j}+\hat{k}).(\hat{i}+2\hat{j}+2\hat{k})}{3\times 3}|=0$
$cos\theta =0$
$\therefore \theta =\frac{\pi }{2}$

Thus, Angle between them is ${90}^o$