The length of the longest interval, in which the function $3 \sin x-4 \sin ^3 x$ is increasing, is

The scalar $\overline{\mathrm{a}} \cdot[(\overline{\mathrm{b}}+\overline{\mathrm{c}}) \times(\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}})]$ equals

The volume of parallelopiped formed by vectors $\hat{i}+m \hat{j}+\hat{k}, \hat{j}+m \hat{k}$ and $m \hat{i}+\hat{k}$ becomes minimum when $m$ is

If the vectors $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\mathrm{mi}+\mathrm{j}+\mathrm{nk}$ are mutually perpendicular, then $(\mathrm{m}, \mathrm{n})$ is