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Orthogonal Vector to a plane

by TG3
Tags: orthogonal, plane, vector
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TG3
#1
Jan13-10, 06:42 PM
P: 66
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?
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Gavins
#2
Jan13-10, 07:27 PM
P: 27
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
TG3
#3
Jan13-10, 08:31 PM
P: 66
Wow, epic fail. Thanks!


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