Question

Define vector product of two vectors.

Answer 1

$$\begin{gathered} \text{If}\overrightarrow{a}\text{and}\overrightarrow{b}\text{are two non-zero non-parallel vectors, then the vector product denoted by}\overrightarrow{a}\text{×}\overrightarrow{b}\text{is defined as}\overrightarrow{a}\times \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\sin \theta \hat{\eta }. \\ \text{Here,}\mathit{\text{θ}}\text{is the angle between}\overrightarrow{a}\text{and}\overrightarrow{b}\text{and}\hat{\eta }\text{is the unit vector perpendicular to the plane of}\overrightarrow{a}\text{and}\overrightarrow{b}\text{such that}\overrightarrow{a}\text{,}\overrightarrow{b}\text{and}\hat{\eta }\text{form a right handed system.} \end{gathered}$$