Question

If a plane cuts off intercepts -6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is

• A. $\frac{1}{\sqrt{61}}$
• B. $\frac{13}{\sqrt{61}}$
• C. $\frac{12}{\sqrt{29}}$
• D. $\frac{5}{\sqrt{41}}$

Answer 1

The correct option is C

$\frac{12}{\sqrt{29}}$

Equation is $\frac{x}{-6}+\frac{y}{3}+\frac{z}{4}=1$ or $-2x+4y+3z=12$
$\therefore$ Length of perpendicular from origin
$=\frac{12}{\sqrt{4+16+9}}=\frac{12}{\sqrt{29}}$