Collinear Operands

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

Since sin θ = 0 when θ = 0 , and the angle between collinear 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 collinear to u (for a scalar k), then:

(ku) × u   =   0.