Find a plane that passes through a point and is perpendicular to 2 planes

multivariable-calculus

Find an equation of a plane that passes through $p(1,5,1)$ and is perpendicular to planes $2x+y-2z = 2$ and $x+3z=4$.

I basically need the 2 other points to make the vector and perform the cross product.

Since $ax+by+cz+d=0$ is the form of a plane. Can I obtain the points as $(a,b,c)$ of the 2 planes given? Also, how can I set them up to obtain the points?


you have two vectors(normals of the given planes) $$u=(2,1,-2), v=(1,0,3)$$ then $n=u×v$
The plane equation is then $$[(x,y,z)-P].n=0$$

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