Define the scalar product of two vectors.
If $\overrightarrow A \times \overrightarrow B=\overrightarrow B \times \overrightarrow A$ then the angle between $\overrightarrow A$ and $\overrightarrow B$ is
The angle between the vectors $\overrightarrow A $ and $\overrightarrow B $ is $\theta .$ The value of the triple product $\overrightarrow A \,.\,(\overrightarrow B \times \overrightarrow A \,)$ is
Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
For any two vectors $\overrightarrow A $ and $\overrightarrow B $, if $\overrightarrow A \,.\,\overrightarrow B = \,\,|\overrightarrow A \times \overrightarrow B |,$ the magnitude of $\overrightarrow C = \overrightarrow A + \overrightarrow B $ is equal to