Two forces of magnitude $3\;N$ and $4\;N$ respectively are acting on a body. Calculate the resultant force if the angle between them is $0^{\circ}$. (in $;N$)

There are two force vectors,one of $5\, N$ and the other of $12\, N$. At what angle should the two vectors be added to get a resultant vector of $17\, N$,$7\, N$,and $13\, N$ respectively?

Prove the associative law of vector addition.

If $|A|=2$ and $|B|=4$ and the angle between them is $60^{\circ}$,then $|A-B|$ is

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

$A$ car travels $6 \, km$ at an angle of $45^o$ north of east and then travels a distance of $4 \, km$ at an angle of $135^o$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east direction?