phys notes

Properties of the cross product We write the cross product between two vectors as [\vec{a} \times \vec{b}] (pronounced "a cross b"). Unlike the dot product, which returns a number, the result of a cross product is another vector. Let's say that [\vec{a} \times \vec{b} = \vec{c}]. This new vector [\vec{c}] has two special properties. First, it is perpendicular to both [\vec{a}] and [\vec{b}]. Phrasing this in terms of the dot product, we could say that [\vec{c} \cdot \vec{a} = \vec{c} \cdot \vec{b} = 0].