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Math Help - finding equation of plane

  1. #1
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    finding equation of plane

    find equation of the plane through points (0,1,1),(1,0,1) and (1,1,0).

    So I'm going to take the cross product of 2 vectors to find the normal. How do I know which two points to use to make the vectors? e.g. <1-0,0-1,1-1>, <1-1,1-0,0-1>, <1-0,1-1,0-1> Depending on what combination I use I will get a differnt normal vector, is this because one normal is on one side of the plane and the other is on the opposite side? If I use differnt normals the equation of the plane will be differnt. Does this mean that the plane can be traced out in two differnt directions or something?
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  2. #2
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    Quote Originally Posted by superdude View Post
    find equation of the plane through points (0,1,1),(1,0,1) and (1,1,0). So I'm going to take the cross product of 2 vectors to find the normal. How do I know which two points to use to make the vectors? e.g. <1-0,0-1,1-1>, <1-1,1-0,0-1>, <1-0,1-1,0-1> Depending on what combination I use I will get a differnt normal vector, is this because one normal is on one side of the plane and the other is on the opposite side? If I use differnt normals the equation of the plane will be differnt. Does this mean that the plane can be traced out in two differnt directions or something?
    Absolutely not in this sense, all the vectors that you get are multiples of each other.
    In other words, they are all parallel.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by superdude View Post
    find equation of the plane through points (0,1,1),(1,0,1) and (1,1,0).

    So I'm going to take the cross product of 2 vectors to find the normal. How do I know which two points to use to make the vectors? e.g. <1-0,0-1,1-1>, <1-1,1-0,0-1>, <1-0,1-1,0-1> Depending on what combination I use I will get a differnt normal vector, is this because one normal is on one side of the plane and the other is on the opposite side? If I use differnt normals the equation of the plane will be differnt. Does this mean that the plane can be traced out in two differnt directions or something?
    It won't matter in the end. the normal vectors you get with different combinations will be parallel.

    I usually try to base them at one point though. So call the first point A, the second B and the third C. Then form the vectors AB and AC. These two vectors are based at A. It gives some structure to the whole thing.
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