If one side of a square is represented by the vector $3i + 4j + 5k,$ then the area of the square is

Find a unit vector in the direction of $\overrightarrow{PQ},$ where $P$ and $Q$ have coordinates $(5, 0, 8)$ and $(3, 3, 2),$ respectively.

If $G$ is the centroid of the $\triangle ABC$,then $\vec{GA} + \vec{GB} + \vec{GC}$ is equal to

If $p = 7i - 2j + 3k$ and $q = 3i + j + 5k,$ then the magnitude of $p - 2q$ is

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $\hat{i}+2 \hat{j}-\hat{k}$ and $-\hat{i}+\hat{j}+\hat{k}$ respectively,in the ratio $2: 1$ externally.

If $O$ is any point and $OA + OB + OC + OD = xOE$,where $ABCD$ is a quadrilateral and $E$ is the point of intersection of the lines joining the mid-points of opposite sides,then find the value of $x$.