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Math Help - Planes problem -help

  1. #1
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    Planes problem -help

    Don't know how I could go solve this question:

    Determine the coordinates of the point where the plane with equation r = (4,1,6) + s[11,-1,3] + t[-7,2,-2] crosses the Z-axis.

    The answer in the text says0,0,5)
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  2. #2
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    Quote Originally Posted by square View Post
    Don't know how I could go solve this question:

    Determine the coordinates of the point where the plane with equation r = (4,1,6) + s[11,-1,3] + t[-7,2,-2] crosses the Z-axis.

    The answer in the text says0,0,5)
    Hi

    A point M(x,y,z) in on the plane iff there exist (s,t) such that
    x = 4 + 11s - 7t
    y = 1 - s + 2t
    z = 6 + 3s - 2t

    M is on the z axis iff x = 0 and y = 0
    This leads to solve a linear system of 2 equations ans 2 unknowns (s and t)
    Then substitute in z
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  3. #3
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    just got the answer, thanks a lot.
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