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Eqn of Plane passing through a point and perpendicular to another plane's trace
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Aug25-08, 06:46 PM
1. The problem statement, all variables and given/known data
Here's the problem:Find the equation of the plane passing through the point (-3,1,4) and perpendicular to the trace of the plane x-3y+7z-3=0 in the xy plane.
2. Relevant equations
to me this should be as easy as finding the two coordiates of the plane's traces on the x and y axis. ie (3,0,0) and (0,-1, 0). Since these two points and the point (-3,1,4) determine the plane.
3. The attempt at a solution
since the general form of the plane is Ax+By+Cz+D=0. I should get 3 equations that look like this:
1) implies that -D/A=3 and thus D=-3 and A=1
substituting into eqn2 yields B=-3
and sunstituing into eqn3 gives C=9/4
so the eqn should be x-3y+9/4Z-3=0 or 4x-12y+9z-3=0
However the answer in the book is 3x+y+8=0. I find that the book is rarely wrong and usually it's me that is confused.
Please advise on where I went wrong
Thanks so much
Aug25-08, 07:37 PM
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