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Math Help - Parametric equations for a plane parallel

  1. #1
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    Parametric equations for a plane parallel

    hey all,

    Having problems trying to find a parametric equation of the plane that is parallel to the plane 3x + 2y -z =1 and passes through the point P(1,1,1).

    I have tried almost all possible (wrong)ways of solving this question. Thanks
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  2. #2
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    Quote Originally Posted by Oiler View Post
    Having problems trying to find a parametric equation of the plane that is parallel to the plane 3x + 2y -z =1 and passes through the point P(1,1,1).
    The plane 3x+2y-z=4 is parallel to the given plane and contains the point (1,1,1).
    What is the parametric equation of that plane?
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  3. #3
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    The parametric equation for the plane is x=t_1, y=t_2, z=3t_1 + 2t_2-1. Not sure how I can get the vectors that go through the point (1,1,1)
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  4. #4
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    Quote Originally Posted by Oiler View Post
    The parametric equation for the plane is x=t_1, y=t_2, z=3t_1 + 2t_2-1. Not sure how I can get the vectors that go through the point (1,1,1)
    Given any plane Ax+By+Cz=D and point P: (p,q,r)
    then the plane Ax+By+Cz=Ap+Bq+Cr is parallel to the given plane and contains P.
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  5. #5
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    Is the problem to "find the plane" or specifically to "find parametric equations for the plane"?

    Any plane parallel to Ax+ By+ Cz= D is of the form Ax+ By+ Cz= E and E can be determined by a single point in the plane.

    You ca get parametric equations for Ax+ By+ Cz= D by, for example, solving for z: z= \frac{D}{C}-\frac{A}{C}x- \frac{B}{C}z and then using x and y as parameters. Or if you prefer using other letters, say u and v,
    x= u

    y= v

    z= \frac{D}{C}-\frac{A}{C}u- \frac{B}{C}v
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