Yes, -(v × u) = -v × u ?
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.
Is the result of u × u perpendicular to both operands?