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Math Help - Planes Point of Intersection

  1. #1
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    Planes Point of Intersection

    a)Determine the equation of the line of intersection L between the planes pi1: 2x+3y-z=3 and pi2: -x+y+z=1.

    b) Determine the point of intersection between L and the xz-plane.

    I need help with part b)

    for part a) my answer is: z=t, x=4t/5, and y=1- (t/5)
    which is correct.
    now for part b) my work thus far is:

    (x,y,z)=(0,0,0)+t(0,1,0) <<< xz-plane means y-axis

    i substituted the parametric equations into symmetric equations

    and I ended up with t=0, then i substituted t=0 into the parametric equation.

    My answer doesn't match the back of the book, can someone tell me what I did wrong. Explain the correct method. Thanks!
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  2. #2
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    The plane y=0 is the xz\text{plane}.
    So I get t=5.
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