# Question #7273c

Mar 6, 2017

$7 J$

#### Explanation:

For a constant force, we say that work, $W$, is:

$W = m a t h b f F \cdot \Delta m a t h b f r$

Here, assuming you mean the particle ends up at $m a t h b f r = \left(x , y , z\right) = \left(2 , - 1 , 0\right)$, this means that:

$W = \left(\begin{matrix}5 \\ 3 \\ 2\end{matrix}\right) \cdot \left(\begin{matrix}2 - 0 \\ - 1 - 0 \\ 0 - 0\end{matrix}\right) = 5 \left(2\right) + 3 \left(- 1\right) + 2 \left(0\right) = 7 J$

I don't wish to complicate this, but we have assumed that the particle moves in a straight line. We do not need to make that assumption as the field is conservative. It just simplifies the calculation.