# Thread: vector parallel and perpendicular to plane

1. ## vector parallel and perpendicular to plane

There is a plane 3x - y +7z = 21

Find a vector parallel, and a vector perpendicular to this plane.

Thanks!

2. A plane has a normal(perpendicular) vector of n=<a,b,c>

Where $\displaystyle ax+by+cz+d=0$

To find a parallel vector, find a vector which is perpendicular to the normal.

The dot product of this vector and the normal vector is 0.

Intuitively, there should be a quick one to come up with.