$(15$pts$)$ The electric field is given by $E=(2xyz)i+(x^{2}z)j+(x^{2}y)k.($Note that units were left off the coefficients to save space$).$ If you move an electron from the origin to the point $(2\mathrm{.}0m,3\mathrm{.}0m,4\mathrm{.}0m)$ along a straight line, what is the change in potential energy?