# Plane Parallel to line

• Jun 23rd 2011, 06:07 PM
IanCarney
Plane Parallel to line
Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t

How would I go about doing this question?
• Jun 23rd 2011, 06:18 PM
Plato
Re: Plane Parallel to line
Quote:

Originally Posted by IanCarney
Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t

A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane.
• Jun 23rd 2011, 06:27 PM
IanCarney
Re: Plane Parallel to line
Quote:

Originally Posted by Plato
A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane.

Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value?
• Jun 23rd 2011, 06:34 PM
Plato
Re: Plane Parallel to line
Quote:

Originally Posted by IanCarney
Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value?

Cross products are not in play here.
Two vectors are perpendicular it their dot product is zero.