Answer
(a) $W = 0$
(b) $W = 75 \times 10^{-5} \,\text{J}$
(c) $W =- 205 \times 10^{-5} \,\text{J}$
Work Step by Step
(a) The work done is related to the angle $\theta = 90^o$ and the distance $d$ by
\begin{aligned}
W&= F d \cos \theta\\
&= E q d \cos \theta \\
\end{aligned}
As $\cos 90^o =0 $, therefore the work done is zero
$$\boxed{W = 0}$$
(b) Upward means the angle $\theta = 0$. Hence, the work done will be
\begin{aligned}
W&= E q d \cos \theta \\
&= \left(4 \times 10^{4} \,\text{V / m} \right)\left(28 \times 10^{-9} \,\text{C} \right)(0.670 \,\text{m}) \cos 0^o\\
&=75 \times 10^{-5} \,\text{J}
\end{aligned}
(c) Downward from the horizontal means the angle $\theta$ is
$$ \theta=180^{\circ} - 45^{\circ} =135^{\circ} $$
\begin{aligned}
W&= E q d \cos \theta \\
&= \left(4 \times 10^{4} \,\text{V / m} \right)\left(28 \times 10^{-9} \,\text{C} \right)(2.6\,\text{m}) \cos 135^o\\
&=\boxed{- 205 \times 10^{-5} \,\text{J}}
\end{aligned}
