Finding Normal Vector for z=2e^(x+y)+8

[Lancelot59]

I need to find the normal vector to:

$$z=2e^{(x+y)}+8$$

So I did the following:

$$-8=2e^{(x+y)}-z$$
$$\nabla F=<2e^{(x+y)},2e^{(x+y)},-1>$$

Did I do this correctly?

 

[grey_earl]

Although it's been a long time since I had this, I think yes. But it's not normalized, I don't know if you need a unit normal vector.
EDIT: Of course it's correct. Just struck me.