6
votes
2answers
109 views

Explanation of a cross product result

In my book the result $$(u\times v)\cdot(x\times y)=\begin{vmatrix} u\cdot x & v\cdot x \\u \cdot y & v \cdot y\end{vmatrix},$$ where u, v, x and y are arbitrary vectors, is stated (here ...
4
votes
1answer
392 views

Cross product of vectors as a determinant: valid matrix operation?

"The definition of the cross product can also be represented by the determinant of a formal matrix." —Wikipedia This seems like a hack to me—something of much practical use but ...