In the given figure,identify which of the vectors are coinitial.

$A$ vector $\vec{r}$ has magnitude $14$ and direction ratios $2, 3, -6$. Find the direction cosines and components of $\vec{r}$,given that $\vec{r}$ makes an acute angle with the $x$-axis.

The position vectors of three points $A, B$ and $C$ are $(1, 3, x), (3, 5, 8)$ and $(y, -1, -6)$ respectively. If $A, B$ and $C$ are collinear, then $(x, y) =$

If $\vec{a} = \hat{i}+\hat{j}-\hat{k}$ and $\vec{b} = 2\hat{i}-3\hat{j}+\hat{k}$ are adjacent sides of a parallelogram,then the lengths of its diagonals are

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

$ABCD$ is a tetrahedron. $\bar{i}-2\bar{j}+3\bar{k}$, $-2\bar{i}+\bar{j}+3\bar{k}$, and $3\bar{i}+2\bar{j}-\bar{k}$ are the position vectors of the points $A, B, C$ respectively. $-\bar{i}+2\bar{j}-3\bar{k}$ is the position vector of the centroid of the triangular face $BCD$. If $G$ is the centroid of the tetrahedron, then $GD=$