Scalar Product of Four Vectors
Category : JEE Main & Advanced
\[\frac{1}{2}|\overrightarrow{CB}\times \overrightarrow{CA}|\] is a scalar product of four vectors. It is the dot product of the vectors \[\mathbf{a}\] and \[\mathbf{c}\times \mathbf{d}\].
It is a scalar triple product of the vectors \[\mathbf{a},\,\mathbf{b}\] and \[\mathbf{c}\,\times \mathbf{d}\] as well as scalar triple product of the vectors \[\mathbf{a}\times \mathbf{b},\,\mathbf{c}\] and d.
\[(\mathbf{a}\times \mathbf{b})\,.\,(\mathbf{c}\times \mathbf{d})\,=\left| \,\begin{matrix} \mathbf{a}.\mathbf{c} & \mathbf{a}\,.\,\mathbf{d} \\ \mathbf{b}.\mathbf{c} & \mathbf{b}\,.\,\mathbf{d} \\ \end{matrix}\, \right|\]
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