If $a = \hat{i} + 2 \hat{j} + 3 \hat{k}$,$b = 2 \hat{i} + 3 \hat{j} + \hat{k}$,$c = 8 \hat{i} + 13 \hat{j} + 9 \hat{k}$ and $x a + y b + z c = 0$,then $\frac{x y}{z^2} =$

$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

If the vectors $\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$ and $\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$ are collinear,then the values of $p$ and $q$ are:

If $ABCDEF$ is a regular hexagon,then $\overrightarrow {AD} + \overrightarrow {EB} + \overrightarrow {FC} = $

If the position vectors of two points $A$ and $B$ are $\vec{a} - 3\vec{b}$ and $6\vec{b} - 2\vec{a}$ respectively,then the position vector of the point dividing $AB$ in the ratio $1 : 2$ is:

Find the unit vector in the direction of vector $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$.