Question

Find the direction cosines of the line $\frac{x+2}{2}=\frac{2y-5}{3};z=-1$.

Answer 1

Equation of line is $\frac{x+2}{2}=\frac{2y-5}{3};z=-1$

$x=\frac{-2}{2}=\frac{y-5/2}{3/2}=\frac{z+1}{0}$

Direction ratio of line are 2,3/2,0.

$\therefore$ Direction cosines of the line are

$\frac{2}{\sqrt{4+\left(9/4\right)+0}},\frac{3/2}{\sqrt{4+9/4+0}},0$

$\Rightarrow \frac{2}{5/2,}\frac{3/2}{5/2},0$

$\Rightarrow$ 4/5,3/5,0