If $C$ is the midpoint of $\overline{AB}$ and $P$ is any point not on $\overline{AB}$,then which of the following is true?

The position vectors of the points $A$ and $B$ are $\vec{a}$ and $\vec{b}$ respectively. If the position vector of the point $C$ is $\frac{\vec{a}}{2} + \frac{\vec{b}}{3}$, then:

$2 \hat{i}-3 \hat{j}+\hat{k}$ and $\hat{i}+2 \hat{j}-3 \hat{k}$ are the position vectors of two points $A$ and $B$ respectively and $C$ divides $AB$ in the ratio $3:2$. If $3 \hat{i}-\hat{j}+2 \hat{k}$ is the position vector of a point $D$, then the unit vector in the direction of $\overrightarrow{CD}$ is

$\hat{i}-2 \hat{j}+\hat{k}$, $2 \hat{i}+\hat{j}-\hat{k}$, and $\hat{i}-\hat{j}-2 \hat{k}$ are the position vectors of the vertices $A, B$, and $C$ of a triangle $ABC$ respectively. If $D$ and $E$ are the midpoints of $BC$ and $CA$ respectively, then the unit vector along $\overrightarrow{DE}$ is

If the length of a vector is $21$ and its direction ratios are $2, -3, 6$,then its direction cosines are:

$<2, 2, 2> = \ldots \ldots$