Question

Find the direction cosines of the line $\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$.

Answer 1

Given, equation of line is $\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$

It can be rewritten as $\frac{x-4}{-2}=\frac{y}{6}=\frac{z-1}{-3}$

Here, drs of the line are $-2,6,-3$.

Now, $\sqrt{(-2{)}^2+6^2+(-3{)}^2}=\sqrt{49}=7units$

Therefore, Dcs of the line are $-\frac{2}{7},\frac{6}{7},-\frac{3}{7}$.