(adsbygoogle = window.adsbygoogle || []).push({}); 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

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

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