Three forces act on a body. Two of them are 5î – 4ĵ N and 3î – 7ĵ. What is the value of the other force for body to be in equilibrium ?

$-2\hat{i} - 3\hat{j}$

For the body to be in equilibrium, the sum of all the forces acting on it must be $zero$.

Let the unknow force by $F$.

Equilibrium condition : $5 \hat{i} - 4\hat{j} - [3\hat{i} - 7\hat{j}] + F = 0$

$\Rightarrow F = -2\hat{i} - 3\hat{j}$