Correct answer: 108
\(\frac{x-2}{1}=\frac{y}{-1}=\frac{z-7}{8}=\lambda\)
\(\frac{\mathrm{x}+3}{4}=\frac{\mathrm{y}+2}{3}=\frac{\mathrm{z}+2}{1}=\mathrm{k}\)
\(\Rightarrow \lambda+2=4 \mathrm{k}-3\)
\(-\lambda=3 \mathrm{k}-2\)
\(\Rightarrow \mathrm{k}=1, \lambda=-1\)
\(8 \lambda+7=\mathrm{k}-2\)
\(\therefore \mathrm{P}=(1,1,-1)\)
Projection of \(2 \hat{i}-2 \hat{k}\) on \(2 \hat{i}+3 \hat{j}+\hat{k}\) is
\(=\frac{4-2}{\sqrt{4+9+1}}\)
\(=\frac{2}{\sqrt{14}}\)
\(\therefore l^{2}=8-\frac{4}{14}=\frac{108}{14}\)
\(\Rightarrow 14 l^{2}=108\)
