Discussion Forum

The angle between the lines   $\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$  and

$\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$

Answer:

Explanation:

Given line,

$\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$  and

$\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$

 Here, a₁=4, b₁=1, c₁=8

 a₂=2, b₂ =2, c₂=1

$\therefore$    $\cos\theta=\frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{(\sqrt{a_1^2+b_1^2+c_1^2})(\sqrt{a_2^2+b_2^2+c_2^2})}$

$\Rightarrow$        $\cos\theta=\frac{8+2+8}{(\sqrt{16+1+64})(\sqrt{4+4+1})}$

$\Rightarrow$       $\cos\theta=\frac{18}{9\times3}=\frac{2}{3}$

 $\Rightarrow$     $\theta=\cos^{-1}\left(\frac{2}{3}\right)$