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Math Help - Vectors: Parametric Equation

  1. #1
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    Vectors: Parametric Equation

    How would I find the direction vector in this problem?

    Find parametric equations for the line that passes through the point (0, -1, 1) and the midpoint of the line segment from (2, 3, -2) to (4, -1, 5).

    Please and thank you
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let M_1(0,-1,1)

    The midpoint is M_2\left(3,1,\frac{3}{2}\right)

    The parametric equations of the line M_1M_2 are:

    \left\{\begin{array}{lll}x=x_1+t(x_2-x_1)\\y=y_1+t(y_2-y_1)\\z=z_1+t(z_2-z_1)\end{array}\right., \ t\in\mathbf{R}
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  3. #3
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    So, would the midpoint be the direction vector of the line?
    The answer to the question is x= 6t, y= -1 + 4t, z= 1 + t so the direction vector here is (6, 4, 1).
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