Answer
(a) $\langle 5, -3 \rangle$
(b) $\langle -5, 3 \rangle$
Work Step by Step
(a) Given $\vec {F_1} =\langle 2, 5 \rangle$ and $\vec {F_2} =\langle 3, -8 \rangle$, the resultant force acting at P is the sum of the forces $\vec {F} =\vec {F_1} + \vec {F_2} =\langle 5, -3 \rangle$
(b) For the forces to be in equilibrium, the additional force required should be $\vec {F_a} =\langle -5, 3 \rangle$
which satisfies the equation $\vec {F} + \vec {F_a} =0$
