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

Answer: (C)

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

Answer 2

Equation is $\frac { x } { - 6 } + \frac { y } { 3 } + \frac { z } { 4 } = 1$ or $- 2 x + 4 y + 3 z = 12$

$\therefore$ Length of perpendicular from origin

$= \frac { 12 } { \sqrt { 4 + 16 + 9 } } = \frac { 12 } { \sqrt { 29 } }$.