$A$ particle is simultaneously acted upon by two forces equal to $4\, N$ and $3\, N$. The net force on the particle is

If $|\vec{a}|=2$ and $|\vec{b}|=3$,find the value of $|3 \vec{a}+2 \vec{b}|$ based on the given figure.

The speed of a particle changes from $\sqrt{5} \ m/s$ to $2\sqrt{5} \ m/s$ in a time $t$. If the magnitude of change in its velocity is $5 \ m/s$,the angle between the initial and final velocities of the particle is (in $^{\circ}$)

Given that $\vec{A} + \vec{B} = \vec{C}$. If $|\vec{A}| = 4, |\vec{B}| = 5$ and $|\vec{C}| = \sqrt{61}$,the angle between $\vec{A}$ and $\vec{B}$ is ....... $^o$

Let $\vec{A}$ and $\vec{B}$ be two non-zero vectors of different magnitudes. Which one of the following is the correct equation?

Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^\circ$. The magnitude of their resultant is