If $\vec{a} = -4\hat{i} + 2\hat{j} - 5\hat{k}$ and $\vec{b} = 12\hat{i} - 6\hat{j} + 15\hat{k}$,then the vectors $\vec{a}$ and $\vec{b}$ are $.......$

$ABCDEF$ is a regular hexagon. Find the sum of the vectors $\vec{BE} + \vec{BC} + \vec{EF} + \vec{BA} + \vec{CF} + \vec{AF}$.

If vectors $\overrightarrow{a}_{1} = x \hat{i} - \hat{j} + \hat{k}$ and $\overrightarrow{a}_{2} = \hat{i} + y \hat{j} + z \hat{k}$ are collinear,then a possible unit vector parallel to the vector $x \hat{i} + y \hat{j} + z \hat{k}$ is ...... .

If the position vectors of the points $A, B, C$ are $i, j, k$ respectively and $P$ is a point such that $\overrightarrow{AB} = \overrightarrow{CP},$ then the position vector of $P$ is

If $\overline{OA} = 3\hat{i} + \hat{j} - \hat{k}$,$|\overline{AB}| = 2\sqrt{6}$ and the direction ratios of $\overline{AB}$ are $1, -1, 2$,then $|\overline{OB}| = $

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a}_1=2 \hat{i}-\hat{j}+\hat{k}$, $\overrightarrow{a}_2=3 \hat{i}-4 \hat{j}-4 \hat{k}$, $\overrightarrow{a}_3=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{a}_4=-\hat{i}+3 \hat{j}+\hat{k}$, then the correct order of $m_1, m_2, m_3$ and $m_4$ is