Answer
a) The resultant force is $\text{4}\mathbf{i}-10\mathbf{j}$.
b) The additional force required for the given forces to be in equilibrium is $-\text{4}\mathbf{i}+10\mathbf{j}$. $$
Work Step by Step
(a)
The given three vectors will be added as follows:
$\begin{align}
& {{F}_{1}}+{{F}_{\text{2}}}+{{F}_{3}}=-2\mathbf{i}+3\mathbf{j}+\mathbf{i}-\mathbf{j}+5\mathbf{i}-12\mathbf{j} \\
& =4\mathbf{i}-10\mathbf{j}
\end{align}$
(b)
The given three vectors can be added as follows:
$\begin{align}
& {{F}_{1}}+{{F}_{\text{2}}}+{{F}_{3}}=-2\mathbf{i}+3\mathbf{j}+\mathbf{i}-\mathbf{j}+5\mathbf{i}-12\mathbf{j} \\
& =4\mathbf{i}-10\mathbf{j}
\end{align}$
