Find the work done moving a particle in the force field:
F = $x^2i + xyj + z^2k$
Along the straight line from $(0,0,0)$ to $(2,1,2)$
I've attempted the question by parameterising the line using the method:
$(1-t)(0,0,0) + t(2,1,2)$ = $(2t,t,2t)$
Is this where I am going wrong?
The part I struggle with in these types of questions is always the parameterisation.
Best Answer
I think you are doing just fine. So you want to integrate from $t=0$ which corresponds to the origin to $t = 1$ which corresponds to the endpoint using the standard definition of work done i.e find $dr$, find the dot product betwen $F$ and $dr$, substitute the parametric form to each variable and integrate.