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Thread: Please help me decide an equation for a plane

  1. #1
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    Please help me decide an equation for a plane

    Decide an equation in general form for a plane that is parallel to the vectors u and v and goes thru the point P=(1, 0, 3).

    Vectors: u=(1, -2, 0) v=(3, -5, 1)

    ---

    If the terminology is incorrect it is because I have tried to translate it from Swedish:
    "Ange, på normalform, en ekvation för det plan som är parallellt med vektorerna u och v och går genom punkten P=(1, 0, 3)"

    I really dont get what I need to do. This is the last of six problems I need to solve for my homework that is due on Thursday. Please help me with this!

    Thanks for reading!
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  2. #2
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    Re: Please help me decide an equation for a plane

    A plane can be written as A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0 where <A, B, C> is a vector perpendicular to the plane and (x_0, y_0, z_0) is a point on the plane. You are already given the point (1, 0, 3) so you only need to determine a vector perpendicular to the plane. Since the plane is perpendicular to the two given vectors, the cross product of the two vectors, which is perpendicular to the two vectors, is perpendicular to the plane. That is, take A, B, and C to be the components of the cross product of u and v and take x_0= 1, y_0= 0, z_0= 3.
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  3. #3
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    Re: Please help me decide an equation for a plane

    Quote Originally Posted by ossianlundberg View Post
    Decide an equation in general form for a plane that is parallel to the vectors u and v and goes thru the point $P=(1, 0, 3)$.

    Vectors: $\vec{u}=<1, -2, 0>~\&~ \vec{v}=<3, -5, 1>$
    OR
    If $\vec{R}=<x,y,z>$ the the plane is $(\vec{u}\times\vec{v}){\cdot}(\vec{R}-<1,0,3>)=0$
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  4. #4
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    Re: Please help me decide an equation for a plane

    Thank you really much! I think I got it!
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