With usual notations, if the angles $A, B, C$ of a $\triangle A B C$ are in $A P$ and $b: c=\sqrt{3}: \sqrt{2}$

$$\int \sin ^{-1} x d x=$$

The integrating factor of the differential equation $x \frac{d y}{d x}+y \log x=x^2$ is

If $\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ and $\mathbf{c}=7 \hat{\mathbf{i}}-\hat{\mathbf{j}}+23 \hat{\mathbf{k}}$ are three vectors, then which of the following statement is true.