Examine whether the following forces are conservative or not, and, if so, determine the potential energy V. F () (x, y, z) = 2xyzex

Examine whether the following forces are conservative or not, and, if so, determine the potential energy V. F (α) (x, y, z) = α 2xyzeˆx + x 2 zeˆy + x 2 yeˆz , F (β) (x, y, z) = β ye−γreˆx + ze−γreˆy + xyeˆz , where r 2 = x 2 + y 2 + z 2 and the constants α, β, and γ