Question

The angle between the lines $3x=6y=2z$ and
$\frac{x-2}{-5}=\frac{y-1}{7}=\frac{z-3}{1}$ is

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

Answer 1

Answer: (D)

The $d$.$r^{\prime }$.$s$ of the first line are $2$, $1$, $3$
$\because d$.$r’s$ of second line are $(-5,7,1)$
Now, $cos\theta =\frac{2\left(-5\right)+\left(1\right)\left(7\right)+\left(3\right)\left(1\right)}{\sqrt{2^2+1^2+3^2}\sqrt{{\left(-5\right)}^2+7^2+1^2}}=0$
$\Rightarrow \theta =\frac{\pi }{2}$