If the position vector of one end of a line segment $AB$ is $2i + 3j - k$ and the position vector of its midpoint is $3(i + j + k)$,then what is the position vector of the other end?

For a triangle $ABC$,if $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$,then the length of the median drawn from vertex $A$ is:

If $a, b$ and $c$ are three non-collinear points and $ka + 2b + 3c$ is a point in the plane of $a, b$ and $c$, then $k =$

If a vector $\vec{r}$ makes equal angles with the axes $OX, OY,$ and $OZ$,find the total number of such vectors $\vec{r}$.

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

Consider two points $P$ and $Q$ with position vectors $\overrightarrow{OP} = 3\vec{a} - 2\vec{b}$ and $\overrightarrow{OQ} = \vec{a} + \vec{b}$. Find the position vector of a point $R$ which divides the line segment joining $P$ and $Q$ in the ratio $2:1$ internally.