Cartesian equation of plane that i perpendicular to plane and contains line
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Oct29-08, 06:52 AM
1. The problem statement, all variables and given/known data
Question states "The plane that contains the line r=<-2,4,3>+t<3,2-1> and is perpendicular to the plane r=<5,0,0>+s<2,1,0>+t<-1,0,1> is:"
Answer is y+2z=10
2. Relevant equations
Cross product and dot product of vectors
3. The attempt at a solution
I found a vector normal to the plane r=<5,0,0>=s<2,1,0>+t<-1,0,1>
by doing the cross product of the two direction vectors is <2,1,0> x <-1,0,1>
than apply rule of n.v=0 ie <1,-2,1> . <x-(-2), y-4, z-3>
to get x+2-2y+8+z-3=0
and so x-2y+z = -7
Not sure what I have done wrong here, could someone explain please?
You found a plane that has normal vector <1, -2, 1>? Then you found a plane that is [b]paralllel[b] to r, not perpendicular to it!