Answer to Question #285940 in Classical Mechanics for RRR

Question

A unit vector normal to the surface z=x^2+y^2

At the point (1,2,5) is

Answer 1

The components of a normal vector to the surface $z=f(x,y)$ at the point $(x_0,y_0,z_0)$ are given by

$${\rm \vec N}=(f'_x(x_0,y_0),f'_y(x_0,y_0),-1)$$

In our case

$${\rm \vec N}=(2x_0,2y_0,-1)=(2,4,-1)$$