As I understand a surface is any function in three dimensions, or a function that contains 3 variables (e.g. f(x,y,z) = x + y + z). However my math teacher gave this example:

I am wondering if the given( and ), really can be considered surfaces even though they are equations, and if the example is correct...Quote:

Find the angle between the surfaces:

at the point P(2,-1,2)

gradient of A = 2xi + 2yj +2zk

gradient of B = 2xi + 2yj - k

at the point P:

gradient of A = 4i - 2j + 4k

gradient of B = 4i - 2j - k

gradA dotted with gradB =

then theta = 54.4 degrees