Find the direction cosines of teh line `(x-2)/2=(2y-5)/(-3),z=-1.` Also, find the vector equation of the line.

Explanation

Equation of line is ` frac{{x}+2}{2}=frac{2 {y}-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+(9 / 4)+0}}, frac{3 / 2}{sqrt{4+9 / 4+0}}, 0`

`
...