Given two lines ${{l}_{1}}:\mathrm{ }\frac{x}{2}=y=z$ and ${{l}_{2}}:\mathrm{ }\frac{x-2}{2}=\frac{-

Question

Given two lines ${{l}_{1}}:\mathrm{ }\frac{x}{2}=y=z$ and ${{l}_{2}}:\mathrm{ }\frac{x-2}{2}=\frac{-1-y}{3}$, $z=1$. Explain why lines ${{l}_{1}}$ and ${{l}_{2}}$ are skew. Find the shortest possible distance between the two lines. Determine the Cartesian equation of the common perpendicular that intersects with ${{l}_{1}}$ as well as with ${{l}_{2}}$.

Accepted Answer

(i) Lines are skew, (ii) $\frac{4}{\sqrt{77}}$ units, (iii) $\frac{77x - 90}{231} = \frac{77y - 45}{154} = \frac{77z - 45}{-616}$

2023 CJC Challenge Yourself Q2

2023 CJC Challenge Yourself Q2

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