Two vectors $\vec A$ and $\vec B$ have magnitudes $2$ and $1$ respectively. If the angle between $\vec A$ and $\vec B$ is $60^o$, then which of the following vectors may be equal to $\frac{{\vec A}}{2} - \vec B$

Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.

Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.

In the light of the above statements, choose the most appropriate answer from the options given below:

$100$  coplanner forces each equal to  $10\,\,N$  act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$

Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

Given that; $A = B = C$. If $\vec A + \vec B = \vec C,$ then the angle between $\vec A$ and $\vec C$ is $\theta _1$. If $\vec A + \vec B+ \vec C = 0,$ then the angle between $\vec A$ and $\vec C$ is $\theta _2$. What is the relation between $\theta _1$ and $\theta _2$ ?

The sum of two forces $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ is $\overrightarrow{\mathrm{R}}$ such that $|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .$ The angle $\theta$ (in degrees) that the resultant of $2 \overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ will make with $\overrightarrow{\mathrm{Q}}$ is