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 $.......$

In a quadrilateral $PQRS$, $A$ divides $SR$ in the ratio $1:3$ and $B$ is the mid-point of $PR$. If $3SR - QR - 3PS - PQ = kAB$, then $k=$

If $A, B, C$ are the vertices of a triangle whose position vectors are $a, b, c$ and $G$ is the centroid of the $\Delta ABC$,then $\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC}$ is

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

If $\vec{r} = 3\hat{i} + 2\hat{j} - 5\hat{k}$,$\vec{a} = 2\hat{i} - \hat{j} + \hat{k}$,$\vec{b} = \hat{i} + 3\hat{j} - 2\hat{k}$,and $\vec{c} = -2\hat{i} + \hat{j} - 3\hat{k}$ such that $\vec{r} = \lambda\vec{a} + \mu\vec{b} + \gamma\vec{c}$,then -

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}$,$\bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$,then the unit vector in the direction of $3 \bar{a}+\bar{b}-2 \bar{c}$ is