Two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other if one is a scalar multiple of the other,i.e.,$\vec{A} = k\vec{B}$. Which of the following pairs of vectors are parallel?

Three forces of $3 \ N$,$4 \ N$,and $12 \ N$ act on a point in mutually perpendicular directions. The magnitude of the resultant force is ........ $N$.

If the vector $\overrightarrow{A} = 2\hat{i} + 4\hat{j} - 5\hat{k}$,find its direction cosines.

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence,the forces $\vec{A}$ and $\vec{B}$ are

What is a vector? How can it be represented?

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.