Answer
a) The resultant force is $9\mathbf{i}-3\mathbf{j}$.
b) Additional force required for the given forces to be in equilibrium is $-9\mathbf{i}+3\mathbf{j}$. $$
Work Step by Step
(a)
The given vectors will be added as follows:
$\begin{align}
& {{F}_{1}}+{{F}_{\text{2}}}=\text{3}\mathbf{i}-5\mathbf{j}+\text{6}\mathbf{i}+\text{2}\mathbf{j} \\
& =9\mathbf{i}-3\mathbf{j}
\end{align}$
So,
${{F}_{1}}+{{F}_{2}}=9\mathbf{i}-3\mathbf{j}$
(b)
The given vectors will be added as follows:
$\begin{align}
& {{F}_{1}}+{{F}_{\text{2}}}=\text{3}\mathbf{i}-5\mathbf{j}+\text{6}\mathbf{i}+\text{2}\mathbf{j} \\
& =9\mathbf{i}-3\mathbf{j}
\end{align}$
So, the additional force required for the given forces to be in equilibrium is negative of the resultant force and that is $-9\mathbf{i}+3\mathbf{j}$.
