The value of $m \in \mathbb{R}$, when angle between the vectors $\overline{\mathrm{p}}=\mathrm{m} y \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overline{\mathrm{q}}=y \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \mathrm{~m} y \hat{\mathrm{k}}$ is obtuse angle, is

The volume of the tetrahedron whose coterminous edges are represented by

$$ \bar{a}=-12 \hat{i}+p \hat{k}, \bar{b}=3 \hat{j},-\hat{k}, \bar{c}=2 \hat{i}+\hat{j}-15 \hat{k} $$

570 cu. units, then $\mathrm{p}=$

The maximum value and minimum value of the volume of the parallelopiped having coterminous edges $\hat{\mathrm{i}}+x \hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{j}}+x \hat{\mathrm{k}}$ and $x \hat{\mathrm{i}}+\hat{\mathrm{k}}$ are respectively

Let $\overline{\mathrm{a}}$ and $\overline{\mathrm{c}}$ be unit vectors at an angle $\frac{\pi}{3}$ with each other. If $(\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{c}})=5$, then $[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]=$