Question

The angle between the following pair of lines:
$\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{x-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$ is $\theta ={\cos }^{-1}\frac{a}{3}$ then $a=$

Answer 1

The drs of given two lines are $2,2,1$ and $4,1,8$

Let the angle between those two lines be $\theta$

We have $cos\theta =\frac{2\times 4+2\times 1+1\times 8}{3\times 9}=\frac{18}{27}=\frac{2}{3}$

Therefore $\theta =co{s}^{-1}\frac{2}{3}$