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Math Help - Three vectors lie in a plane

  1. #1
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    Three vectors lie in a plane

    Can i just find the triple scalar product a.(b x c)

    And if it = 0 then it lies in the plane?
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  2. #2
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    Quote Originally Posted by adam_leeds View Post
    Can i just find the triple scalar product a.(b x c) = 0 then it lies in the plane?
    Yes this is true for three non-zero vectors.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Yes this is true for three non-zero vectors.
    Thanks

    So for v1 = (−2, 2, 0), v2 = (6, 1, 4) and v3 = (2, 0,−4)

    The cross product is 58
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  4. #4
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    I don't understand what you are doing.

    v_1\cdot(v_2\times v_3)=72
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  5. #5
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    Quote Originally Posted by Plato View Post
    I don't understand what you are doing.

    v_1\cdot(v_2\times v_3)=72
    Yeah i did something wrong, i used this to help me thanks
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  6. #6
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    A short cut for the triple product is this:
    If v_1= <x_1, y_1, z_1>, v_2= <x_2, y_2, z_2>, and [tex]v_3= <x_3, y_3, z_3> then the cross product is the determinant:
    v_1\cdot(v_2\times v_3)= \left|\begin{array}{ccc}x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{array}\right|
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