Find the equation of the tangent plane to the level surface
x^2 + y^2 - z^2 + 2xyz = 24
at the point (3, -2, -1)


Answer. The is of the form F(x,y,z) = x^2 + y^2 - z^2 + 2xyz = constant.
grad f = < 2x + 2yz, 2y + 2xz, -2z + 2xy>
grad f(3, -2, -1) = < 2(3)+2(-2)(-1), 2(-2)+2(3)(-1), -2(-1)+2(3)(-2)>
grad f(3, -2, -1) = < 6+4, -4-6, 2+-12> = <10, -10, -10>

So we can use <1, -1, -1> as the normal and the equation is

	1(x-3) -1(y+2) -1(z+1) = 0
	x - y - z = 6