Answer
(a) $-4j$
(b) $4j$
Work Step by Step
(a) Given $\vec {F_1} =4i-j$, $\vec {F_2} =3i-7j$, $\vec {F_3} =-8i+3j$, and $\vec {F_4} =i+j$, the resultant force acting at P is the sum of the forces $\vec {F} =\vec {F_1} + \vec {F_2} + \vec {F_3} +\vec {F_4} =-4j$
(b) For the forces to be in equilibrium, the additional force required should be $\vec {F_a} =4j$
which satisfies the equation $\vec {F} + \vec {F_a} =0$
