A pair of skew lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\mathbf{r}=\left( \begin{matrix} -1

Question

A pair of skew lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\mathbf{r}=\left( \begin{matrix} -1 \ 1 \ 3 \ \end{matrix} ight)+\lambda \left( \begin{matrix} -2 \ 2 \ 1 \ \end{matrix} ight)$, $\lambda \in \mathbb{R}$ and $\mathbf{r}=\left( \begin{matrix} 1 \ 3 \ 2 \ \end{matrix} ight)+\mu \left( \begin{matrix} 3 \ 1 \ 6 \ \end{matrix} ight)$, $\mu \in \mathbb{R}$ respectively. Suppose the points $P$ and $Q$ lie on ${{l}_{1}}$ and ${{l}_{2}}$ respectively such that $PQ$ is the shortest distance between ${{l}_{1}}$ and ${{l}_{2}}$ , find the length of $PQ$. [4] (Hint: What relationship(s) does $\overrightarrow{PQ}$ have with ${{l}_{1}}$ and ${{l}_{2}}$?)

Accepted Answer

$\frac{6}{41}\sqrt{410}$ units\)

Shortest Distance Between 2 Skew Lines

Shortest Distance Between 2 Skew Lines

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