If $|\vec A + \vec B| = |\vec A| + |\vec B|$,then the angle between $\vec A$ and $\vec B$ will be ....... $^o$.

$\overrightarrow{A} = 4\hat{i} + 3\hat{j}$ and $\overrightarrow{B} = 4\hat{i} + 2\hat{j}$. Find a vector parallel to $\overrightarrow{A}$ but with a magnitude five times that of $\overrightarrow{B}$.

$A$ particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$. The displacement vector 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.

$A$ particle has a displacement of $12 \, m$ towards east,$5 \, m$ towards north,and $6 \, m$ vertically upward. The magnitude of the resultant displacement is ......... $m$.

Can the resultant of three vectors of unequal magnitudes be a zero vector?