Question

Find direction ratios of line $\perp$ to the lines whose direction ratios are $-2,1,-1$ and $-3,-4,1$

Answer 1

Let $a,b,c$ be the direction ratio of the line.

Given this line is $\perp$ to the lines whose direction ratios are $-2,1,-1$ and $-3,-4,1$. Then,

$-2a+b-c=0$ and $-3a-4b+c=0$.

Then using cross-multiplication we get,

$\frac{a}{1-4}=\frac{b}{3+2}=\frac{c}{8+3}$

or, $\frac{a}{-3}=\frac{b}{5}=\frac{c}{11}$.

Then the direction ratios of the line will be $-3,5,11$.