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Math Help - Vector Equation of a Plane

  1. #1
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    Vector Equation of a Plane

    Find a vector perpendicular to both i+2j-k and 3i-j+k. Hence find the Cartesian equation of the plane parallel to both i+2j-k and 3i-j+k which passes through the point (2,0,-3).

    I managed to solve the first one but not the parallel part.

    Explanation with the aid of diagram is much appreciated. Thanks in advance
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  2. #2
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    Re: Vector Equation of a Plane

    Quote Originally Posted by Jin0730 View Post
    Find a vector perpendicular to both i+2j-k and 3i-j+k. Hence find the Cartesian equation of the plane parallel to both i+2j-k and 3i-j+k which passes through the point (2,0,-3).

    I managed to solve the first one but not the parallel part.

    Explanation with the aid of diagram is much appreciated. Thanks in advance
    If u~\&~v are non-parallel vectors and P: (a,b,c) then (u\times v)\cdot<x-a,y-b,z-c>=0 is a plane which contains P and is parallel to u~\&~v.
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  3. #3
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    Re: Vector Equation of a Plane

    Different way of saying the same thing: if <A, B, C> is a vector perpendicular to both vectors u and v, then A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0 is a plane parallel to both u and v and passing through (x_0, y_0, z_0).
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