A volcano just erupted and lava is streaming down from the m

A volcano just erupted and lava is streaming down from the mountain top. Suppose that the altitude of the mountain is given by

where h is the maximum height, and suppose also that lava flows in the direction of steepest descent (fastest change in z). Find

Solution

a) The projection of the point (x,y,z) on the xy-plane is the point (x,y,0) which implies projection point is (1,2,0).

b) z = 0

he^{-(x2 + 2y2)} = 0