# Eqn of Plane passing through a point and perpendicular to another plane's trace

by Stumbleinn
Tags: passing, perpendicular, plane, point, trace
 P: 1 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) 3A+D=0 2) -B+D=0 3) -3A+B+4C+D=0 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
Math
Emeritus