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
$a \times 0+b \times 2+c \times 1=0$
$\Rightarrow -a+2 b+2 c=0$ and $0 a+2 b+c=0$
$\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) .