# Plane tangent to sin(xyz) = x + 2y + 3z

I'm trying to solve the following :

Find the tangeant plane to sin(xyz) = x + 2y + 3z at P(2,-1,0)

Fx = 1 - cos(xyz)*yz = 1 Fy = 2 - cos(xyz)*xz = 2 Fz = 3 - cos(xyz)*xy = 5

So my gradient would be i + 2j + 5k And my plane would be 0 = x + 2y + 5z

But the manual says that the answer is 4x-y-2z = 6... So I'm kinda lost!

• Answer keys are sometimes wrong. Are you sure the problem numbers match? – amd Dec 5 '18 at 20:13
• Yeah, but they are often mistakes in this manual. It seems to be the case here. Thanks! – Cappuccino Dec 5 '18 at 20:18

$$F_x(x-x_0)+F_y(y-y_0)+F_z(z-z_0)=0$$
$$1(x-2)+2(y+1)+5(z-z_0)=0$$ or
$$x+2y+5z=0$$