Physics - Vectors Question with Solution | TestHub

$(\overrightarrow{\mathbf{B}}\times \overrightarrow{\mathbf{A}})\cdot \overrightarrow{\mathbf{A}}$ $\begin{array}{rl}& =BA\cos \theta \overrightarrow{\mathbf{n}}\cdot \overrightarrow{\mathbf{A}}\\ & =0\end{array}$ 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, $(\overrightarrow{\mathbf{B}}\times \overrightarrow{\mathbf{A}})\cdot \overrightarrow{\mathbf{A}}=\overrightarrow{\mathbf{B}}\cdot (\overrightarrow{\mathbf{A}}\times \overrightarrow{\mathbf{A}})=0(\because \overrightarrow{\mathbf{A}}\times \overrightarrow{\mathbf{A}}=0)$ 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 $(\overrightarrow{\mathbf{A}}\times \overrightarrow{\mathbf{A}})\cdot \overrightarrow{\mathbf{A}}$