We have an ellipsoid with the equation 4x^2 + y^2+ 4z^2 = 16, and it is raining. Gravity will make the raindrops slide down the dome as rapidly as possible. I have to describe the curves whose paths the raindrops follow. This is probably more vector calculus than physics, but i wasn't sure how to solve it, so i don't know if knowledge of physics is necessary. I found the gradient, and i know that the rain will probably flow where the gradient is largest; however, i don't know how to go on.