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Math Help - Help with parametric equation

  1. #1
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    Help with parametric equation

    Find parametric equations for the line of intersection of the two planes.
    P1: 2x − y + z = 1 P2 : x − y + z = 2
    <2,-1,1> X <1,-1,1> = <0,-1,1>

    x = -1
    y=t
    z=3+t

    I don't know how the book gets this answer.
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  2. #2
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    Quote Originally Posted by khuezy View Post
    Find parametric equations for the line of intersection of the two planes.
    P1: 2x − y + z = 1 P2 : x − y + z = 2
    <2,-1,1> X <1,-1,1> = <0,-1,1>

    x = -1
    y=t
    z=3+t

    I don't know how the book gets this answer.
    Solve simultaneously:

    2x − y + z = 1 .... (1)

    x − y + z = 2 .... (2)

    (1) - (2): x = -1.

    Substitute into x = -1 into either (1) or (2):

    − y + z = 3.

    Now let y = t, say, where t \in R and solve for z.
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