Thread: gradient vectors

A drop of water falls on the surface (x^6)y +(x^4)(z^2)+(y^2)(z^3)= 79 at the point (-1, 3, 2). Find a three-dimensional unit vector in the direction that the water will begin to flow, assuming that the water will flow in the steepest downhill direction.

What is your difficulty? You title this "gradient vectors" so presumably you know that the gradient vector always point in the direction of greatest increase so that it negative always point in the direction of greatest decrease. And, that, of course, is the direction the water will flow.