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 $\mathrm{p}=$

With usual notations, the perimeter of a triangle ABC is 6 times the arithmetic mean of sine of its angles. If $\mathrm{a}=1$, then $\angle \mathrm{A}=$

The angle between the lines whose direction cosines are $\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}$ and $\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}$ is

If $\sin \left(\frac{\pi}{4} \cot \theta\right)=\cos \left(\frac{\pi}{4} \tan \theta\right)$, then the general solution of $\theta$ is