Consider the curve given $by$ the parametrization:

$r(t)=(\sqrt[\phantom{2}]{2}t,e^t,e^{-t})$ for tin$[0,).$

Now, Suppose that you are $at$ the point $(0,1,1)$ and subjected $to$ a force given $by$:

$F(x,y,z)=(\frac{-x}{(x^2+y^2+z^2{)}^{\frac{3}{2}}},\frac{-y}{(x^2+y^2+z^2{)}^{\frac{3}{2}}},\frac{-z}{(x^2+y^2+z^2{)}^{\frac{3}{2}}}),(It\text{'}s$ very similar $to$ gravity$)$

How much work will you $do$ traveling along the curve from $(0,1,1)to(\sqrt[\phantom{2}]{2},e,e^{-1})?$

Make sure $to$ provide a clear, complete, and detailed solution. $If$ you use any theorems, state which ones you are

using clearly and also show why those theorems are appropriate $to$ this problem.