If the position vectors of $A$ and $B$ are respectively $(1, 1, 0)$ and $(0, 1, 1)$,then $\overrightarrow{AB} =$

Show that the vectors $2 \hat{i}-3 \hat{j}+4 \hat{k}$ and $-4 \hat{i}+6 \hat{j}-8 \hat{k}$ are collinear.

The perimeter of the triangle whose vertices have the position vectors $\hat{i}+\hat{j}+\hat{k}$,$5\hat{i}+3\hat{j}-3\hat{k}$,and $2\hat{i}+5\hat{j}+9\hat{k}$ is

In a quadrilateral $PQRS$,$M$ and $N$ are mid-points of the sides $PQ$ and $RS$ respectively. If $\vec{PS} + \vec{QR} = t \vec{MN}$,then $t =$

$\hat{i}-2 \hat{j}+\hat{k}$,$2 \hat{i}+\hat{j}-\hat{k}$,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 $m_1, m_2, m_3$ 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