The common principal solution of the equations $\sin \theta=-\frac{1}{2}$ and $\tan \theta=\frac{1}{\sqrt{3}}$ is

The slopes of the lines represented by $6 x^2+2 \mathrm{hxy}+y^2=0$ are in the ratio $2: 3$, then $\mathrm{h}=$

If $\theta$ is an obtuse angle between vectors $\bar{a}$ and $\overline{\mathrm{b}}$ such that $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{~b}}|=3$ and $|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=5 \sqrt{5}$ then $\bar{a} \cdot \bar{b}=$

If the plane $\frac{x}{2}-\frac{y}{3}-\frac{\mathrm{z}}{5}=1$ cuts the co-ordinate axes in points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ respectively, then the area of the triangle $A B C$ is