# Equation of a plane parallel to two vectors.

• Jan 9th 2012, 01:48 AM
dipsy34
Equation of a plane parallel to two vectors.
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].

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
• Jan 9th 2012, 02:01 AM
FernandoRevilla
Re: Equation of a plane parallel to two vectors.
Hint $\displaystyle (1,2,3)\times (2,3,-1)=(-11,7,-1)$ .
• Jan 9th 2012, 02:57 AM
dipsy34
Re: Equation of a plane parallel to two vectors.
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?
• Jan 9th 2012, 03:02 AM
FernandoRevilla
Re: Equation of a plane parallel to two vectors.
Quote:

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?

$\displaystyle -11(x-2)+7(y-3)-(z-1)=0$
• Jan 9th 2012, 03:02 AM
Plato
Re: Equation of a plane parallel to two vectors.
Quote:

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