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)

$\sqrt{14}$

Answer 2

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