Explanation

(c) $\mathbf{r}_{\mathbf{i}} = ( - 3.0\ m)\widehat{\mathbf{i}} + (2.0\ m)\widehat{\mathbf{j}} + (8.0\ m)\widehat{\mathbf{k}}$
$r_{f} = (9.0\ m)\widehat{\mathbf{i}}\mathbf{+}(2.0\ m)\widehat{\mathbf{j}}\mathbf{+}( - 8.0\ m)\widehat{\mathbf{k}}$
$\therefore$Displacement $= \mathbf{r}_{f} - \mathbf{r}_{i}$
$= \left\lbrack (9.0\ m)\widehat{\mathbf{i}} + (2.0\ m)\widehat{\mathbf{j}} + ( - 8.0\ m)\widehat{\mathbf{k}} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ - \lbrack( - 3.0m)\widehat{\mathbf{i}} + (2.0m)\widehat{\mathbf{j}} + (8.0m)\widehat{\mathbf{k}}\mathbf{\rbrack}$
$= \left\lbrack (12.0m)\widehat{\mathbf{i}} - (16.0m)\widehat{\mathbf{j}} \right\rbrack$