Find an Equation of Plane Through P (3,3,1) Perpendicular to Planes

[Giuseppe]

Hello, can anyone help me with this problem?

Find an equation of the plane through P (3,3,1) that is perpendicular to the planes x +y = 2z and 2x +z =10

Thanks

 

[amcavoy]

First take the two planes you have. The normal to the first is the vector <1,1,-2>. The normal to the second is <2,0,1>. Since both of these will essentially be parallel to the plane you are looking for, you want to find the vector perpendicular to that plane. In other words, the binormal vector to <1,1,-2> and <2,0,1>. How do you do that in a 3 dimensional coordinate system? Try using the cross product, and assuming you know how to get the equation of a plane from the normal vector and a point, you shouldn't have any trouble arriving at an answer.