Cross Product

A common operation between two ${\mathbb{R}}^3$ vectors. $u\times v=(u_2{v}_3-u_3{v}_2,u_3{v}_1-u_1{v}_3,u_1{v}_2-u_2{v}_1)$

Properties

• Linearity : $(au+bv)\times w=a(u\times w)+b(v\times w)$
• Alternating : $(u\times v)=-(v\times u)$
• Dependence detecting : $\{u,v\}$ dep $⟹u\times v=0$