# Orthogonal Vector to a plane

1. Jan 13, 2010

### TG3

The problem statement, all variables and given/known data

Find a nonzero vector orthogonal to the plane through points P (0, -2, 0) Q (4, 1, -2) and R (5,3,1) and find the area of the triangle formed by PQR.

The attempt at a solution
To be honest, I am not entirely sure how to do this problem. I've looked through my textbook and notes, but there is no example that is of the same form of this problem. However, I suspect the cross product is important:

PQ has a vector of <4,3,-2>
RP has a vector of <5,5,1>

Trying to find the cross product I get:
(3--6) - (4-10) + (20 - 15)
Equals 20.

Is that right, and what do I do from here?

2. Jan 13, 2010

### Gavins

You're on the right track. Those 2 vectors you have are parallel to your plane. If you compute the cross product between them, you will get a new vector perpendicular to the 2 vectors and hence perpendicular to the plane. Do you know how to compute the cross product? What you get should be a vector. The next bit relies on the geometric definition of the cross product.

Go over on computing the cross product as it's all you'll need.
http://en.wikipedia.org/wiki/Cross_product

3. Jan 13, 2010

### TG3

Wow, epic fail. Thanks!