Let $G$ be the centroid of a triangle $ABC$ and $O$ be any other point in that plane,then $\overline{OA}+\overline{OB}+\overline{OC}+\overline{OG}=$

Classify the following measure as a scalar or a vector:
$2 \text{ meters north-west}$

Let $A, B$ and $C$ be three points on a circle of radius $R$. If $O$ is the centre of the circle and $\angle AOB = 45^{\circ}, \angle BOC = 45^{\circ}$,then the resultant of $\vec{OA}, \vec{OB}$ and $\vec{OC}$ has magnitude

If $P(1, 3, -7)$ and $Q(5, -2, 4)$,then $|\vec{PQ}| = \dots$

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point on the line $PQ$ such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

If $\hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}+2 \hat{j}+\hat{k}$ are sides of a parallelogram,then a unit vector parallel to one of the diagonals of the parallelogram is