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Math Help - eq. of line in space.

  1. #1
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    eq. of line in space.

    Give two points A and B in 3d space with co-ordinates:
    A(a,b,c) and B(a',b',c'), what is the equation of the line passing through both points?

    Thanks for the help.
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  2. #2
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    See this maybe it helps.

    The parametric equations for a line passing through (x_1, y_1, z_1), (x_2, y_2, z_2) are:
    \begin{cases}x = x_1 + (x_2 - x_1)\cdot t \\<br />
        y = y_1 + (y_2 - y_1)\cdot t\\<br />
        z = z_1 + (z_2 - z_1)\cdot t \end{cases}
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  3. #3
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    Quote Originally Posted by james_bond View Post
    See this maybe it helps.

    The parametric equations for a line passing through (x_1, y_1, z_1), (x_2, y_2, z_2) are:
    \begin{cases}x = x_1 + (x_2 - x_1)\cdot t \\<br />
        y = y_1 + (y_2 - y_1)\cdot t\\<br />
        z = z_1 + (z_2 - z_1)\cdot t \end{cases}
    You can also write a line in three dimensions in "symmetric" form.
    Solving each of those equations, for t,

    \frac{x- x_1}{x_2- x_1}= \frac{y- y_1}{y_2- y_1}= \frac{z- z_1}{z_2- z_1}


    I notice you asked for "the" equation of a line in three dimensions. Because a line is only one dimension, you need to "reduce" two dimensions and so need either two equations (3- 2= 1), as I give or introduce a new parameter, t, giving 4 variables with 3 equations: 4- 3= 1.
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