A plane inR

3

has Cartesian equation

5x+8y+11z=11

.

has Cartesian equation If we let F[z, y, z) = 5: + 8y + 112 then the partial derivatives are 3F _ me- . 313:! _ I Number I . = Number 33, i | . g1: : I Number I These are the components of the normal to the plane' which is the vector 6:: BF VP 2 3y E 82 Now consider a surface in R3 with Cartesian equation 322+5y2+2=11 Ifwe let G'[z,y,z] : 3:2 + 5y2 + 2. the partial derivatives are 3G .. - 35 =Iilnl . 592'; : I In. I 32 = I In-' These are the components of VG' the normal to the surface at the point [:,y, 2], In contrast to the plane, the normal to a general surface need not be constant