The direction ratios of the line of intersection of the planes $x-y+z-5=0$ and $x-3 y-6=0$, are

The distance between the line $\overline{\mathrm{r}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ and the plane $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=4$ is

If $y=\sin ^2\left(\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

$$ \int \frac{\sin x}{\sqrt{5 \sin ^2 x+6 \cos ^2 x}} d x $$