Question

The distance of the point $P(4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to :

• A. $2\sqrt{3}$
• B. $\sqrt{14}$
• C. 3
• D. $\sqrt{6}$

Answer 1

Answer: (B)

Equation of line is $\frac{x+3}{3}=\frac{y-2}{3}=\frac{z-3}{-1}=\lambda$
$M(3\lambda -3,3\lambda +2,3-\lambda )$
D.R of PM( $3\lambda -7,3\lambda -4,5-\lambda )$
Since PM is perpendicular to line
$\Rightarrow 3(3\lambda -7)+3(3\lambda -4)-1(5-\lambda )=0$
$\Rightarrow \lambda =2$
$\Rightarrow M(3,8,1)\Rightarrow PM=\sqrt{14}$