Find the coordinates of the point (x, y, z) on the plane z = 2 x + 1 y + 4 which is closest to the origin.

x =

y =

z =

HINT. You need to minimize the distancedfrom the origin to the point(x,y,z). Equivalently, you can minimize d2, which is simpler. Expressd2(which depends on(x,y,z)) in terms ofx,yonly; then minimize that function ofxandy.