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).
