The lines [(x-2)/(2)=(y)/(-2)=(z-7)/(16)] and [(x+3)/(4)=(y+2)/(3)=(z+2)/(1)] intersect at…

Question

The lines $$\frac{x-2}{2}=\frac{y}{-2}=\frac{z-7}{16}$$ and $$\frac{x+3}{4}=\frac{y+2}{3}=\frac{z+2}{1}$$ intersect at the point $P$. If the distance of $$\mathrm{P}$$ from the line $$\frac{x+1}{2}=\frac{y-1}{3}=\frac{z-1}{1}$$ is $l$, ...

Answer: 108

Accepted Answer

$\begin{gathered} \frac{x-2}{1}=\frac{y}{-1}=\frac{z-7}{8}=\lambda \ \frac{x+3}{4}=\frac{y+2}{3}=\frac{z+2}{1}=k \ \Rightarrow \lambda +2=4k-3 \ -\lambda =3k-2 \ \Rightarrow k=1,\lambda =-1 \ 8\lambda +7=k-2 \ 	herefore P=(1,1,-1) \end{gathered}$

Projection of $2\hat{i}-2\hat{k}$ on $2\hat{i}+3\hat{j}+\hat{k}$ is

$\begin{gathered} =\frac{4-2}{\sqrt{4+9+1}}=\frac{2}{\sqrt{14}} \ 	herefore {l}^{2}=8-\frac{4}{14}=\frac{108}{14} \ \Rightarrow 14{l}^{2}=108 \end{gathered}$

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