Question

The angle between the lines $\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}$ and $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is A $\frac{\pi }{2}$

The direction ratios of $\frac{x-5}{7}=\frac{y+2}{-5}=\frac{z}{1}$ are $7,-5,1.$
and the direction ratios of $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ are $1,2,3.$
$\text{Let}\theta$ be the angle between the lines.
$\text{Then,}\cos \theta =\frac{7\times 1+(-5)\times 2+1\times 3}{\sqrt{7^2+(-5{)}^2+1^2}\sqrt{1^2+2^2+3^2}}$
$\Rightarrow \cos \theta =0$
$\Rightarrow \theta =\frac{\pi }{2}$