$A$ particle moving with velocity $\overrightarrow{V}$ is acted upon by three forces represented by the vector triangle $PQR$. The velocity of the particle will

Three forces $\vec{P}, \vec{Q},$ and $\vec{R}$ act at a point in a plane. The angles between $\vec{P}$ and $\vec{Q}$,and $\vec{Q}$ and $\vec{R}$ are $150^{\circ}$ and $120^{\circ}$ respectively. What is the ratio of the magnitudes of the forces $\vec{P}, \vec{Q},$ and $\vec{R}$ if the system is in equilibrium?

$A$ man of mass $50 \,kg$ carries a bag of weight $40 \,N$ on his shoulder. The force with which the floor pushes up his feet will be ......... $N$.

$A$ body under the action of several forces will have zero acceleration:

$A$ particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (assuming the particle is initially at rest):
$\vec{F}_1 = 5\hat{i} - 5\hat{j} + 5\hat{k}$
$\vec{F}_2 = 2\hat{i} + 8\hat{j} + 6\hat{k}$
$\vec{F}_3 = -6\hat{i} + 4\hat{j} - 7\hat{k}$
$\vec{F}_4 = -\hat{i} - 3\hat{j} - 2\hat{k}$
Then the particle will move:

Mr. $A, B$ and $C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in a railway yard. If they apply forces $F_1, F_2$ and $F_3$ respectively on ropes,then for which set of forces at that instant will they be able to perform the said job?