# Thread: Plane Parallel to line

1. ## 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?

2. ## Re: Plane Parallel to line

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.

3. ## Re: Plane Parallel to line

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?

4. ## Re: Plane Parallel to line

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.