Question

Direction cosines of the line which is perpendicular to the lines whose direction ratios are 1, –1, 2 and 2, 1, –1 are given by :

• A. $[\frac{-1}{\sqrt{35}},\frac{5}{\sqrt{35}},\frac{3}{\sqrt{35}}]$
• B. $[\frac{-1}{\sqrt{35}},\frac{-5}{\sqrt{35}},\frac{3}{\sqrt{35}}]$
• C. $[\frac{1}{\sqrt{35}},\frac{5}{\sqrt{35}},\frac{-3}{\sqrt{35}}]$
• D. $[\frac{1}{\sqrt{35}},\frac{-7}{\sqrt{35}},\frac{-3}{\sqrt{35}}]$

Answer 1

The correct option is A $[\frac{-1}{\sqrt{35}},\frac{5}{\sqrt{35}},\frac{3}{\sqrt{35}}]$

If l, m, n are the d.c.’s of the line which is perpendicular to the given lines, then
l – m + 2n = 0 and 2l + m –n = 0
$\therefore \frac{l}{1-2}=\frac{m}{4+1}=\frac{n}{1+2}\Rightarrow \frac{l}{-1}=\frac{m}{5}=\frac{n}{3}$.
so d.r's =$(-1,5,3)$