The Cartesian equation of the plane $$\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$ is

The principal solutions of $$\sqrt{3} \sec x+2=0$$ are

$$\int \operatorname{cosec}(x-a) \operatorname{cosec} x d x=$$

If $$f(x)=2x^3-15x^2-144x-7$$, then $$f(x)$$ is strictly decreasing in