# Vectors and crossproducts

SigmaCrisis
I'm given three points in 3D space (vectors), P, Q, and R. So I have to find a vector that is perpendicular to the plane formed by these points.

Anyone? Thanks.

I really just need some hint(s) for this.

whozum
Draw two vectors from any of the points to other points. Only one plane defines those two vectors. The cross product of those two vectors is an orthogonal vector to that plane.

SigmaCrisis
Umm, sorry, but could you elaborate? I don't quite get it...new to Calc III.

Homework Helper
if p,q are two points, subtracting Q-P gives a vector pointing from P to Q.

Thus if P,Q,R are 3 points, spanning a plane, the two vectors Q-P and Q-R are both parellel to that plane.

then there is a construction called cross product for finding sa vector perpendiculr to two given vectors. hence perpendiculr to the plane they are parallel to.

thus (Q-P) x (Q-R) is perpendicualr to the plane spanned by P,Q,R.

SigmaCrisis
Thanks a bunch!

SigmaCrisis
One more thing, I'm also asked to find the area of the triangle PQR.

Staff Emeritus