Question

Plane through A(1,-2,1) perpendicular to the vector from origin to A.

Answer 1

(1, -2, 1) is perpendicular/normal to the plane, and passes through the point (1, -2, 1), so its equation is

$(x-1,y+2,z-1)\cdot(1,-2,1)=0\imples(x-1)-2(y+2)+(z-1)=0\implies\boxed{x-2y+z=6}$