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