Question

Find direction cosine line $x=3z+2,y=2-5z$.

Answer 1

Given line is $x=3z+2,y=2-5z$
$\therefore \frac{x-2}{3}=z;\frac{y-2}{-5}$
$\therefore \frac{x-2}{3}=\frac{y-2}{-5}=\frac{z}{1}$
Now compate with standard equation
Direction of line $\overline{l}=(3,-5,1)$
$\left|\overline{l}\right|=\sqrt{9+25+1}=\sqrt{35}$
$\therefore$ Direction cosines of given line
$=\frac{\overline{l}}{\left|\overline{l}\right|}=\frac{(3,-5,1)}{\sqrt{35}}=(\frac{3}{\sqrt{35}},\frac{-5}{\sqrt{38}},\frac{1}{\sqrt{35}})$