Equation of a plane parallel to two vectors.

**dipsy34** · January 9th 2012, 01:48 AM

A plane goes trough a point and is parallel to two vectors what is the general equation?

The plane goes trough the point [2,3,1] and is parallel to the two vectors [1,2,3] and [2,3,-1].

The answer is 11x-7y+z-2=0

If I do the cross product of the two vectors I get the vector [-11,7,-1] which if multiplied by -1 corresponds to the answer but I dont thin that's the right way. :P

**FernandoRevilla** · January 9th 2012, 02:01 AM

Hint $(1,2,3)\times (2,3,-1)=(-11,7,-1)$ .

**dipsy34** · January 9th 2012, 02:57 AM

Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?

**FernandoRevilla** · January 9th 2012, 03:02 AM

Originally Posted by dipsy34

Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?

$-11(x-2)+7(y-3)-(z-1)=0$

**Plato** · January 9th 2012, 03:02 AM

Originally Posted by dipsy34

Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?

If $U~\&~V$ are two non-parallel vectors and $P$ is a point. Let $R=<x,y,z>$ then $(U\times V)\cdot(R-P)=0$ is a plane parallel to the vectors that contains the point.

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