I'm having trouble starting off this question. Any help would be appreciated!
"Lisa is trying to hold on to her toy car.
Her sister Ruby is pulling with a force of 8 N on a bearing of 023° and her brother Mark with a force of 5 N on a bearing of 155°.
What force does Lisa need to exert to keep the toy in equilibrium?"
The forces need to sum up to zero to prevent they toy from moving. The forces exerted by Ruby respectively Mark are $$ F_R = 8\begin{pmatrix}\cos 23^\circ \\ \sin 23^\circ\end{pmatrix},\, F_M = 5\begin{pmatrix}\cos 155^\circ \\ \sin 155^\circ\end{pmatrix}. $$ so Lisa will have to apply the force $$ F_L = -F_R - F_M \text{,} $$ because then $$ F_L + F_R + F_M = 0 \text{.} $$