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Mathematics-Online problems:

Interactive Problem 121: Distance Point/Line and Line/Line

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Given the points $ P=(0,3,-2)$, $ Q=(3,7,-1)$ and $ R=(1,-3,-1)$ in $ \mathbb{R}^3$. Let $ g_1$ be the line through $ P$ and $ Q$, and let $ g_2$ be the line through $ R$ with direction

$\displaystyle \vec{v}= \begin{pmatrix}1 \\ 0 \\ 1 \end{pmatrix} \; . $

Find the distance of $ P$ from $ g_2$, and the distance between $ g_1$ and $ g_2$.

Solution:

Distance of $ P$ from $ g_2$: .

Distance between $ g_1$ and $ g_2$: .
   

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  automatically generated: 2/ 6/2018