Position vectors of the particles are $${r_1} = - 2\hat i + 5\hat j\,\,{\text{and}}\,\,{r_2} = 4\hat j + 3\hat k$$
∴ Displacement of the particle, $$\Delta s = {r_2} - {r_1}$$
$$\eqalign{ & = 4\hat j + 3\hat k - \left( { - 2\hat i + 5\hat j} \right) \cr & = 2\hat i - \hat j + 3\hat k \cr} $$
Force on the particle, $$F = 4\hat i + 3\hat j\,N$$
∴ Work done, $$W = F \cdot \Delta s = \left( {4\hat i + 3\hat j\,} \right) \cdot \left( {2\hat i - \hat j + 3\hat k} \right)$$
$$ = 8 - 3 = 5\,J$$