Let $u$ and $v$ be two vectors in $R^2$. If $|u+v|^2=2(|u|^2+|v|^2)$,then .....

Classify the following as scalar and vector quantities:
Force

If the position vectors of the points $A$ and $B$ are $2 \hat{i}+3 \hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+2 \hat{k}$ respectively,then the unit vector along $\overrightarrow{BA}$ and in the direction of $\overrightarrow{AB}$ is

If $ABCDEF$ is a regular hexagon and $\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} = p\vec{AD} = q\vec{AO}$, where $O$ is the center of the hexagon, then the values of $p$ and $q$ respectively are

If the position vectors of points $A, B, C$ are respectively $\hat{i}, \hat{j}, \hat{k}$ and $\vec{AB} = \vec{CX}$,then the position vector of point $X$ is:

$P$ is the point of intersection of the diagonals of the parallelogram $ABCD$. If $O$ is any point,then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} + \overrightarrow{OD} = $