A particle moving with velocity \(\vec{\text{V}}\) is acted by three forces shown by the vector triangle PQR. The velocity of the particle will be:

CONCEPT:

Force- Force is defined as the push or pull of the object with a mass that causes it to change its velocity is called a force. Newton's second law, states the product of mass and acceleration and it is written as;

F = ma       -----(1)

and acceleration is defined as the ratio of the velocity to the time taken by the object and it is written as;

\(\vec a = \frac{d\vec v}{dt}\)       -----(2)

Here, F is the force, m is the mass, v is the velocity and a is acceleration.

EXPLANATION:

When a particle moves with the velocity \(\vec{\text{V}}\) is acted by the three forces as shown in the figure below;

As forces are forming a closed loop in the same order therefore their net force is equal to zero.

\(So,{{\vec F}_{net}} = 0\)     ------(3)

Now, on putting the value of equation 2) in equation 3) we have;

\( \Rightarrow m\frac{{d\vec v}}{{dt}} = 0\)

\( \Rightarrow \vec V = constan t\)

Hence, option 3) is the correct answer.