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Orthogonal Vector to a plane 
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#1
Jan1310, 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: (36)  (410) + (20  15) Equals 20. Is that right, and what do I do from here? 


#2
Jan1310, 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 


#3
Jan1310, 08:31 PM

P: 66

Wow, epic fail. Thanks!



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