If the angle between the vectors A and B is θ , the value of the...

$(\overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{A}}) \cdot \overrightarrow{\mathbf{A}}$$\begin{aligned} & =B A \cos \theta \overrightarrow{\mathbf{n}} \cdot \overrightarrow{\mathbf{A}} \\ & =0\end{aligned}$$$Here$\hat{\mathbf{n}}$is perpendicular to both$\overrightarrow{\mathbf{A}} and \overrightarrow{\mathbf{B}}$. Alternative :$(\overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{A}}) \cdot \overrightarrow{\mathbf{A}}$Interchange the cross and dot, we have,$(\overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{A}}) \cdot \overrightarrow{\mathbf{A}}=\overrightarrow{\mathbf{B}} \cdot(\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{A}})=0 \quad(\because \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{A}}=0)$NOTE: The volume of a parallelopiped bounded by vectors$\overrightarrow{\mathbf{A}}, \overrightarrow{\mathbf{A}} and \overrightarrow{\mathbf{A}}$can be obtained by giving formula$(\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{A}}) \cdot \overrightarrow{\mathbf{A}}$