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

Quote:

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Originally Posted by Oiler

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).

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The plane is parallel to the given plane and contains the point .
What is the parametric equation of that plane?

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)

Quote:

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Originally Posted by Oiler

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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Given any plane and point
then the plane is parallel to the given plane and contains .

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: and then using x and y as parameters. Or if you prefer using other letters, say u and v,