Question

A plane passes through $(2,3,-1)$ and is perpendicular to the line having direction ratios $3,-4,7$. The perpendicular distance from the origin to this plane is

• A. $\frac{13}{\sqrt{74}}$
• B. $\frac{5}{\sqrt{74}}$
• C. $\frac{6}{\sqrt{74}}$
• D. $\frac{14}{\sqrt{74}}$

Answer 1

The correct option is A $\frac{13}{\sqrt{74}}$

Direction ratios of $\perp$er is $3,-4$ & $7$.

So, Eqn of plane will be $3x-4y+7z+d=0$

It passes through $(2,3,-1)$.

So, $6-12-7+d=0$

$\therefore$ eqn is $3x-4y+7z+13=0$

Perpendicular distance from origin $=\frac{|13|}{\sqrt{9+16+49}}=\frac{13}{\sqrt{74}}$