The distance of the point P(4,6,-2) from the line passing through the point (-3,2,3) and p…

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:

Accepted Answer

$\overrightarrow{A P}=7 \hat{i}+4 \hat{j}-5 \hat{k} \Rightarrow|\overrightarrow{A P}|=\sqrt{49+16+25}=\sqrt{90} A N$

$=$ projection of $\overrightarrow{A P}$ on $\vec{b}=\overrightarrow{A P} \cdot \vec{b}=\frac{21+12+5}{\sqrt{19}}=\frac{38}{\sqrt{19}}$

$(P N)^{2}=(A P)^{2}-(A N)^{2}=90-76=14 \Rightarrow P N=\sqrt{14}$

Solutions · 1