My name is Alexander FufaeV and here I write about:
Cross Product of Two Vectors Explained Simply
The cross product, also known as the vector product, is a mathematical operation between two vectors \( a \) and \(b\) in three-dimensional space. The cross product is often represented with the symbol "×". The result of the cross product is a vector \( a \times b\) that is perpendicular to the plane spanned by the two initial vectors.
$$ \begin{align} \boldsymbol{a} ~\times~ \boldsymbol{b} ~=~ \begin{bmatrix} a_2b_3-a_3b_2 \\ a_3b_1-a_1b_3 \\ a_1b_2-a_2b_1 \end{bmatrix} \end{align} $$
The magnitude \( |a \times b| \) of the cross product can be written with the angle \( \varphi \) as follows: