Question

The distance of the point having position vector $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line passing through the point $(2,3,-4)$ and parallel to the vector, $6\hat{i}+3\hat{j}-4\hat{k}$ is :

• A. $6$
• B. $7$
• C. $2\sqrt{13}$
• D. $4\sqrt{3}$

Answer 1

The correct option is B $7$

Given,
$\overrightarrow{n}=6\hat{i}+3\hat{j}-4\hat{k}$
$\overrightarrow{PQ}=-3\hat{i}-\hat{j}+10\hat{k}$
$PR=\left|\frac{\overrightarrow{PQ}\cdot \overrightarrow{n}}{|\overrightarrow{n}|}\right|=\frac{61}{\sqrt{61}}=\sqrt{61}$
$PQ=\sqrt{110}$

$RQ=\sqrt{P{Q}^2-P{R}^2}$
$=\sqrt{110-61}$
$=7$