Edit made on September 30, 2013 by ColinWright at 17:02:31
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HEADERS_END
The vector cross-product is an operation that takes two vectors and produces another. It is non-associative and non-commutative.
A vector cross-product can be computed by taking the determinant of a matrix:
** EQN:\b{a}{\times}\b{b}=\left|\begin{matrix}\b{i}&\b{j}&\b{k}\\a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right|=\b{i}(a_2b_3-a_3b_2)-\b{j}(a_1b_3-a_3b_1)+\b{k}(a_1b_2-a_2b_1)=\left[\begin{matrix}a_2b_3-a_3b_2\\-(a_1b_3-a_3b_1)\\a_1b_2-a_2b_1\end{matrix}\right] |>> [[[ EQN:{\bf~a}\times{\bf~b}=\left|\begin{matrix}{\bf~i}&{\bf~j}&{\bf~k}\\a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right|={\bf~i}(a_2b_3-a_3b_2)-{\bf~j}(a_1b_3-a_3b_1)+{\bf~k}(a_1b_2-a_2b_1)=\left[\begin{matrix}a_2b_3-a_3b_2\\-(a_1b_3-a_3b_1)\\a_1b_2-a_2b_1\end{matrix}\right] ]]] <<|
where *a* is the vector EQN:\left[\begin{matrix}a_1\\a_2\\a_3\end{matrix}\right] , *b* is the vector
EQN:\left[\begin{matrix}b_1\\b_2\\b_3\end{matrix}\right] and *i,* *j* and *k* are unit vectors.