14.2: Cross Product

The cross product â × ˆb of two vectors is defined as a vector ĉ that is perpendicular to both â and ˆb. Its direction is given by the right-hand rule and its magnitude is equal to the area of the parallelogram that the vectors span.

Let â = (a₁, a₂, a₃)^T and ˆb = (b₁, a₂, a₃) be two vectors in R³ . Then, their cross product â × ˆb is given by

\[\hat{a}\times \hat{b}=\begin{pmatrix}
a_{2}b_{3}-a_{3}b_{2}\\
a_{3}b_{1}-a_{1}b_{3}\\
a_{1}b_{2}-a_{2}b_{1}
\end{pmatrix} \]

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