The unit vectors that define a coordinate system have the following properties relative to the cross product: \[\begin{aligned} \vec x \times \vec y &= \vec z\\ \vec y \times \vec z &= \vec x\\ \vec z...The unit vectors that define a coordinate system have the following properties relative to the cross product: \[\begin{aligned} \vec x \times \vec y &= \vec z\\ \vec y \times \vec z &= \vec x\\ \vec z \times \vec x &= \vec y\\\end{aligned}\] For these properties to be correct, it should be noted that the direction of the \(z\) axis in three dimensions is specified by the choice of \(x\) and \(y\) axes.
