Orthogonal Vector to a plane


by TG3
Tags: orthogonal, plane, vector
TG3
TG3 is offline
#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?
Phys.Org News Partner Science news on Phys.org
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance
Gavins
Gavins is offline
#2
Jan13-10, 07:27 PM
P: 26
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
TG3 is offline
#3
Jan13-10, 08:31 PM
P: 66
Wow, epic fail. Thanks!


Register to reply

Related Discussions
orthogonal projection of 2 points onto a plane Differential Geometry 5
Orthogonal Projection onto XY plane Calculus 9
Finding a vector orthogonal to others Linear & Abstract Algebra 18
A-orthogonal vector set Linear & Abstract Algebra 4
Equation of a plane orthogonal to a vector Introductory Physics Homework 46