Find a vector normal to the plane at (2,1,7)

[mharten1]

Homework Statement

This is a two part problem
A) Find a vector normal to the plane at (2,1,7)
B) Find a vector normal to the plane tangent to the paraboloid at (2,1,7)

Homework Equations

Plane: z = x + y +4
Paraboloid: z = x^2 +3y^2

The Attempt at a Solution

I'm not sure where to start. I know that a vector normal to the plane is <1,1,-1>, but that isn't at (2,1,7). Any help?

 

[Dick]

A plane has the same normal everywhere, doesn't it?

 

[mharten1]

A plane has the same normal everywhere, doesn't it?

That's what I thought at first. But it seems too easy to be the solution to both questions. I'm going to read over the section again and see if I can find anything that will be useful.

 

[Dick]

That's what I thought at first. But it seems too easy to be the solution to both questions. I'm going to read over the section again and see if I can find anything that will be useful.

It's not the solution to the second question. Think about using the gradient.

 

[mharten1]

It's not the solution to the second question. Think about using the gradient.

I was able to solve it, thank you. :)