Question

The distance of the point $2 \mathbf { i } + \mathbf { j } - \mathbf { k }$ from the plane

$\mathbf { r } . ( \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k } ) = 9$ is+

• A. $\frac { 13 } { \sqrt { 21 } }$
• B. $\frac { 3 } { \sqrt { 21 } }$
• C. $\frac { 13 } { 21 }$
• D. $\frac { 13 } { 3 \sqrt { 21 } }$

Answer 1

Answer: (A)

$\frac { 13 } { \sqrt { 21 } }$

Answer 2

We know that the perpendicular distance of a point P with position vector $\mathbf { a }$ from the plane is given by

.

Here $\mathbf { a } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k } , \mathbf { n } = \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k }$ and $d = 9$.

So, required distance $= \frac { | ( 2 \mathbf { i } + \mathbf { j } - \mathbf { k } ) \cdot ( \mathbf { i } - 2 \mathbf { j } + 4 \mathbf { k } ) - 9 | } { \sqrt { 1 + 4 + 16 } }$

$= \frac { | 2 - 2 - 4 - 9 | } { \sqrt { 21 } } = \frac { 13 } { \sqrt { 21 } }$.