Question

Find the direction cosines of the line: $\frac{x-1}{2}=-y=\frac{z+1}{2}$

Answer 1

Given,

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

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

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

Here, direction ratios are 2, -1 , 2

$\Rightarrow a=2,b=-1,c=2$

So, the direction cosines (Dc's)are given as,

$\frac{2}{\sqrt{2^2+(-1{)}^2+2^2}},\frac{-1}{\sqrt{2^2+(-1{)}^2+2^2}},\frac{2}{\sqrt{2^2+(-1{)}^2+2^2}}$

$[\because \frac{a}{\sqrt{a^2+b^2+c^2}},\frac{b}{a^2+b^2+c^2},\frac{c}{a^2+b^2+c^2}]$

$\frac{2}{\sqrt{4+1+4}},\frac{-1}{\sqrt{4+1+4}},\frac{2}{\sqrt{4+1+4}}$

$\Rightarrow \frac{2}{\sqrt{9}},\frac{-1}{\sqrt{9}},\frac{2}{\sqrt{9}}$

$D{c}^{\prime }s\Rightarrow \frac{2}{3},\frac{-1}{3},\frac{2}{3}$ Answer