Question

The direction ratios of the normal to the plane passing through the points $(1,-2,3),(-1,2,-1)$ and parallel to the line $\frac{x-2}{2}=\frac{y+1}{3}=\frac{z}{4}$ are proportional to.

• A. $2:3:4$
• B. $4:0:7$
• C. $-2:0:-1$
• D. $2:0:-1$

Answer 1

Answer: (D)

$2:0:-1$

The equation of a plane passing through $(1,-2,3)$ is $a(x-1)+b(y+2)+c(z-3)=0$ ........(i)

It passes through $(-1,2,-1)$ and is parallel to the given line.

$\therefore a(-2)+b\left(4\right)+c(-4)=0$
and $2a+3b+4c=0$

$\Rightarrow \frac{a}{28}=\frac{b}{0}=\frac{c}{-14}$

$\Rightarrow \frac{a}{2}=\frac{b}{0}=\frac{c}{-1}$

Hence, $a:b:c=2:0:-1$.