Four forces act on a point particle. Three of them are $2\hat{i} + 3\hat{j}$, $-\hat{i} - 2\hat{j}$,

Question

Four forces act on a point particle. Three of them are $2\hat{i} + 3\hat{j}$, $-\hat{i} - 2\hat{j}$, and $4\hat{i} + \hat{j}$. If the particle is in equilibrium, the fourth force is

Professor PC Thomas Classes · Answer

For equilibrium, $\vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \vec{F}_4 = 0$. Sum of first three is $(2-1+4)\hat{i} + (3-2+1)\hat{j} = 5\hat{i} + 2\hat{j}$. So, $5\hat{i} + 2\hat{j} + \vec{F}_4 = 0 \implies \vec{F}_4 = -5\hat{i} - 2\hat{j}$.