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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 :
Option: 1
$\sqrt{14}$

Option: 2
3

Option: 3
$\sqrt{6}$

Option: 4
$2 \sqrt{3}$

Answers (1)

best_answer

equation of line

$\overline{\mathrm{r}}=(-3,2,3)+\lambda(3,3,-1)$
$\overline{\mathrm{PM}} \cdot(3,3,-1)=0$
$(3 \lambda-7,3 \lambda-4,5-\lambda) \cdot(3,3,-1)=0$
$\Rightarrow 3(3 \lambda-7)+3(3 \lambda-4)-1(15-\lambda)=0$
$\Rightarrow 19 \lambda=38 \Rightarrow \lambda=2$

$\mathrm{M}=(3,8,1)$
$\mathrm{PM}=\sqrt{1+4+9}=\sqrt{14}$
$(-3+3 \lambda, 2+3 \lambda, 3-\lambda)$

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