The direction of magnetic force on the electron as shown in the diagram is along,

In figure, magnetic field direction due to current carrying wire is along  $\left(-\widehat{k}\right)$ into the page.
So, magnetic force,  $\overrightarrow{F}=q\overrightarrow{V}X\overrightarrow{B}$ 
$\overrightarrow{F}=(-e)(-V\widehat{i})X(-B\widehat{k})=-e\left(V\widehat{i}XB\widehat{k}\right)=-e\left(VXB\right)\left(\widehat{i}X\widehat{k}\right)=-e\left(VB\right)(-\widehat{j})=e\left(VB\right)\widehat{j}$