### Three Dimensional Geometry Question 8

#### Question 8 - 25 January - Shift 1

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 :

(1) 3

(2) $\sqrt{6}$

(3) $2 \sqrt{3}$

(4) $\sqrt{14}$

## Show Answer

#### Answer: (4)

#### Solution:

#### Formula: Equation of a straight line

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}$

Therefore, the correct answer is option (4).