Colinear Operands

The length of u × v is |u| |v| sin θ. If u and v are colinear (parallel) what is the length of their cross product?

Since sin θ   =   0 when θ   =   0 , and the angle between colinear vectors is zero, the magnitude of the result is zero. The result is still a vector; it is the zero vector  0.

u × u   =   0.

Also, since ku is colinear to u (for a scalar k), then:

(ku) × u   =   0.