If a unit vector is represented as $\overrightarrow{u} = 0.4 \hat{i} + 0.7 \hat{j} + c \hat{k}$,then the value of '$c$' is

If the vector $\vec{P} = 3\hat{i} + 4\hat{j} + 12\hat{k}$,then the magnitude of the vector $\vec{P}$ is ......

The angle between the two vectors $\vec A = 3\hat i + 4\hat j + 5\hat k$ and $\vec B = 3\hat i + 4\hat j + 5\hat k$ is ....... $^o$

$A$ vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radian $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$. In that case,$|\vec{B} - \vec{A}|$ is

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 $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{AD}=2\overrightarrow{AO}$.
In the light of the above statements,choose the most appropriate answer from the options given below.

The resultant of $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec{B}$. Which of the following is correct?