In each situation below, three forces are acting on a particle. Given two of the forces and the fact the particle is in equilibrium, find the third force.

\(\mathbf{a} = \quantity{-3\mathbf{i} + 2\mathbf{j}}{N}\)

\(\mathbf{b} = \quantity{4\mathbf{i} + \mathbf{j}}{N}\)

\(\mathbf{a}\) has magnitude \(\quantity{10}{N}\) and direction \(45^{\circ}\) anticlockwise from the positive \(x\) axis

\(\mathbf{b}= \quantity{6\mathbf{i} - 3\mathbf{j}}{N}\)

Is it possible to use a different approach for each situation?