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Math Help - Calc III Vector Problems

  1. #1
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    Calc III Vector Problems

    Determine an equation of the plane containing the following points: (2,0,2), (4,3,1), and (0,1,3).

    Do I set up a cross-product?
    Last edited by riverjib; November 25th 2007 at 08:53 PM. Reason: Other problems are more urgent than this one.
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  2. #2
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    Quote Originally Posted by riverjib View Post
    Determine an equation of the plane containing the following points: (2,0,2), (4,3,1), and (0,1,3).

    Do I set up a cross-product?
    Try Google first.

    RonL
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  3. #3
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    Hello, riverjib!

    Determine an equation of the plane containing the points: . A(2,0,2),\;B(4,3,1),\;C(0,1,3)
    Yes, we need a cross-product . . . but are you just guessing?
    . . Do you have any idea why?


    To write the equation of a plane, we need a point on the plane, (x_1,y_1,z_1)
    . . (we have 3 to choose from), and the normal vector of the plane, \vec n \,=\,\langle a,b,c\rangle.
    Then substitute into: . a(x-x_1) + b(y - y_1) + c(z-z_1) \:=\:0


    We have: . AB \:=\:\langle2,3,-1\rangle,\;\;AC \:=\:\langle -2,1,1\rangle

    . . Then: . \vec n \;=\;\begin{vmatrix}i & j & k \\ 2 & 3 & \text{-}1 \\ \text{-}2 & 1 & 1 \end{vmatrix} \;=\;i(3+1) -j(2-2) + k(2+6) \;=\;4i + 8k

    Hence: . \vec n \;=\;\langle4,0,8\rangle \;=\;\langle1,0,2\rangle


    Can you finish the problem now?

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