Question

Direction ratios of the line which is perpendicular to the lines with direction ratios $-1,2,2$ and $0,2,1$ are

• A. $1,1,2$
• B. $2,-1,2$
• C. $-2,1,2$
• D. $2,1,-2$

Answer 1

The correct option is B $2,-1,2$

Let $l,m,n$ be the direction ratios of the required line

Given : $l,m,n$ are perpendicular to $-1,2,2$

So, their dot product will be zero

$⟹l(-1)+m\left(2\right)+n\left(2\right)=0$

$⟹-l+2m+2n=0$ .... $\left(i\right)$

Also, $l,m.n$ are perpendicular to $0,2,1$

$⟹2m+n=0$

$⟹m=-\frac{n}{2}$

Substituting $m$ in $\left(i\right)$ we get

$-l-n+2n=0⟹l=n$

So, the direction ratios are in proportion to $n:-\frac{n}{2}:n$

Simplifying we get $2,-1,2$

Thus, the direction ratios are $2,-1,2$.