$ABCDEF$ is a regular hexagon whose centre is $O$. Then, $\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF}$ is equal to (in $\vec{AO}$)

If $A(1, 2, 1), B(2, 3, 2), C(2, 1, 3), D(3, 2, 4)$,then the directions of $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are $.......$

If $\theta$ is the interior angle of a regular pentagon,then $|(\sin \theta) \hat{i}+(\cos \theta) \hat{j}+(\tan \theta) \hat{k}|=$

If the magnitudes of $\bar{a}$,$\bar{b}$ and $\bar{a}+\bar{b}$ are respectively $3$,$4$ and $5$,then the magnitude of $\bar{a}-\bar{b}$ is

If $\overline{r} = -4 \hat{i} - 6 \hat{j} - 2 \hat{k}$ is a linear combination of the vectors $\overline{a} = -\hat{i} - 4 \hat{j} + 3 \hat{k}$ and $\overline{b} = -8 \hat{i} - \hat{j} + 3 \hat{k}$,then which of the following is true?

Let $PQRS$ be a quadrilateral. If $M$ and $N$ are midpoints of the sides $PQ$ and $RS$ respectively,then $\overrightarrow{PS} + \overrightarrow{QR} =$