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Math Help - Simple parametrization problem

  1. #1
    Junior Member
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    Sep 2009
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    Simple parametrization problem

    How do I parametrize a straight line segment from (2,-1,3) to (4,2,-1)?

    How do I parametrize path C from (0,0,0) to (4,2,3) that consists of three line segments parallel to x, y and z-axis in that order?

    How do I parametrize path C from (-1,2,-2) to (1,5,2) that consists of three line segments parallel to the z-axis, x-axis, and y-axis in that order?

    These are probably simple but I really need help
    Last edited by messianic; December 5th 2009 at 11:25 AM.
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    When we move from (2,-1,3) to (4,2,-1), the following changes take place:

    x increases 2 units
    y increases 3 units
    z decreases 4 units

    Now let's say we want the independent variable of the parametrized line, t, to range from 0 to 1, so that as t moves from 0 to 1, the point (x(t),y(t),z(t)) will move from (2,-1,3) to (4,2,-1). In that case, since

    (x,y,z)=(2,-1,3)

    at t=0, we obtain for our parametrization

    (x,y,z)=(2+2t,-1+3t,3-4t).

    Hint for the next problem: the first line of the path is given by

    (x,y,z)=(4t,0,0).
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