How do you find the acute angle between surfaces?

Question

For instance, I'm trying to figure out the acute angle between the surfaces:
x(y^2)z = 3x + z^2 and 3x^2 - y^2 + 2z = 1 at the point (1,-2,1).

Any help would be appreciated. Thanks! :)

Answer 1

Ugh, messy problem. Do both partial differentiations for each surface function, then use the tangents to define a pair of vectors at (1,2,-1) for each surface function. Do vector cross products to find the normal vectors at (1,2,-1) for each surface function. Do a vector dot product of the normal vectors to find the angle. I suppose I could actually work all of this out, but today is Labor Day.

See Wolfram site on how to figure out normal vectors, given a surface function.