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 k**u** is collinear to **u** (for a scalar k), then:

(ku)×u=0.

Is the result of
**u** **×** **u**
perpendicular to
both operands?