$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. Find $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=.......$

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is

Two forces of magnitude $8 \,N$ and $15 \,N$ respectively act at a point. If the resultant force is $17 \,N$, the angle between the forces has to be .......

Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$

$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.

A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60 \,m$, then the magnitude of displacement would be$.....\,m$ (Given $\left.\cos 135^{\circ}=-0.7\right)$