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Math Help - Shortest distance between skew lines

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    Shortest distance between skew lines

    Say I have 2 skew lines and they've given me the equations of the lines as well as shortest distance between the lines. How would I find the points on the 2 lines, e.g. A on line 1 and B on line 2 such that AB is the shortest distance.
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Say I have 2 skew lines and they've given me the equations of the lines as well as shortest distance between the lines. How would I find the points on the 2 lines, e.g. A on line 1 and B on line 2 such that AB is the shortest distance.
    1. Draw a sketch.

    2. A with \vec a lies on l_1 that means: \vec a = \overrightarrow{p_1} + k \cdot \vec u.

    B with \vec b lies on l_2 that means: \vec b = \overrightarrow{p_2} + t \cdot \vec v.

    The vector \overrightarrow{AB} is collinear to (\vec u \times \vec v)

    3. Solve for (k, t, s):

    <br />
\left( \overrightarrow{p_2} + t \cdot \vec v \right) - \left( \overrightarrow{p_1} + k \cdot \vec u \right) = s \cdot (\vec u \times \vec v)
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