If the position vectors of $A$ and $B$ are $i + 3j - 7k$ and $5i - 2j + 4k$,then the direction cosine of $\overrightarrow{AB}$ along the $y$-axis is

Let the position vectors of two points $A$ and $B$ be $\vec{a}+\vec{b}+\vec{c}$ and $\vec{a}-2\vec{b}+3\vec{c}$,respectively. If the points $P$ and $Q$ divide $AB$ in the ratio $1:3$ internally and externally respectively,then $3|AB|=$

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}| = $

The points whose position vectors are $2\hat{i}+3\hat{j}+4\hat{k}$, $3\hat{i}+4\hat{j}+2\hat{k}$, and $4\hat{i}+2\hat{j}+3\hat{k}$ are the vertices of

If $\overrightarrow{AB} = 2\hat{i} + 3\hat{j} - 6\hat{k}$ and $\overrightarrow{BC} = 6\hat{i} - 2\hat{j} + 3\hat{k}$ are the vectors along two sides of a triangle $ABC$,then the perimeter of triangle $ABC$ is:

$<2, 2, 2> = \ldots \ldots$