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Math Help - Euclidean spaces - nonparametric equation of a plane

  1. #1
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    Smile Euclidean spaces - nonparametric equation of a plane

    I'm trying to study Euclidean spaces and one of the exercises is to derive the nonparametric equation for the following plane:
    x = 2 - 3s + t
    y = 4
    z = 1 + s + t
    I tried to write a new equation expressed in terms of x and y only:-
    t = x - 2 + 3s = z -1 - s
    However, I was stuck because I couldn't solve for s and t.
    The textbook lists answer y=4 as the answer. Why? Please help me understand! Thank you!
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  2. #2
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    Quote Originally Posted by math beginner View Post
    I'm trying to study Euclidean spaces and one of the exercises is to derive the nonparametric equation for the following plane:
    x = 2 - 3s + t
    y = 4
    z = 1 + s + t
    I tried to write a new equation expressed in terms of x and y only:-
    t = x - 2 + 3s = z -1 - s
    However, I was stuck because I couldn't solve for s and t.
    The textbook lists answer y=4 as the answer. Why? Please help me understand! Thank you!
    Eliminate the variables s and t in the system of simultaneous equations:

    [1]: x = 2 - 3s + t
    [2]: y = 4 + 0s + 0t
    [3]: z = 1 + s + t

    Calculate s and t using [1] and [3] and plug the results into [2]

    If you now feel as if someone has made a practical joke you can use the cross-product of (-3, 0, 1) \times (1, 0, 1)=(0,4,0) to determine the equation of the plane.
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