Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$

Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$

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

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

Two forces $F_1 = 3N$ at $0^o$ and $F_2 = 5N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of ………. $N$

The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled then the resultant is also doubled. The angle between the two forces is  ……….. $^o$

Let the angle between two nonzero vectors $\overrightarrow A $ and $\overrightarrow B $ be $120^°$ and resultant be $\overrightarrow C $