Finding the equation of a plane passing through 3 pointsby Luscinia Tags: finding equations, linear algebra, plane and vector, plane equation 

#1
Mar3112, 06:37 PM

P: 11

1. The problem statement, all variables and given/known data
Find the equation of the plane passing through point A(2,1,0), B(3,1,5) and C(2,2,1) 2. Relevant equations Um..I don't know? 3. The attempt at a solution Vector AB=(3 1 5)^T(2 1 0)^T=(1 2 5)^T Vector AC=(2 2 1)^T(2 1 0)^T=(0 1 1)^T perpendicular vector n= vector ABxvector AC=(2*15*1 5*01*1 1*12*0)^T=(7 1 1) since n=(a b c)^T will give a plane with equation ax+by+cz=d, I had assumed the equation of the plane would therefore be 7xy+z=d, but it turns out it's actually 7x+yxz=15 Why are the signs inverted? (I sort of missed a few classes so I may be unaware of some fundamental concepts here) and how do I find d (which turns out to be 15) 



#2
Mar3112, 06:43 PM

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#3
Mar3112, 08:24 PM

P: 329

Getting to "d": take one point and solve for d to put it in the plane. If you use a different d, you get a parallel plane. So if you generate d for one point, you can check it with another (both of the others, if you're nervous ).




#4
Apr112, 04:52 PM

P: 11

Finding the equation of a plane passing through 3 points
Oh man, can't believe I didn't see that. Thanks!



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