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

Answer: (B)

Let direction ratios of a line be $(a,b,c)$.
Since, line is perpendicular to the direction
rations (-1,2,2) and (0,2,1) .
$\therefore a\times -1+b\times 2+c\times 2=0$ and
$a\times 0+b\times 2+c\times 1=0$
$\Rightarrow -a+2b+2c=0$ and $0a+2b+c=0$
$\Rightarrow \frac{a}{2-4}=\frac{-b}{-1-0}=\frac{c}{-2-0}$
$\Rightarrow \frac{a}{-2}=\frac{b}{1}=\frac{c}{-2}$
or $\frac{a}{2}=\frac{b}{-1}=\frac{c}{2}$
Hence, direction ratio of a line is (2,-1,2) .