By examining the diagram, or working with the formula: (ku) × v = k( u × v )
Fussing with math gives the result:
| (ku) × v | = | ku | | v | sin θ = | k | |u | | v | sin θ
The magnitude is | k | times the magnitude of u × v and the direction must be the same.
Another fact is that, in general, (u × v) × w ≠ u × (v × w)
To see this, look at the diagram and mentally form the cross product (u × v) , then take the cross product of that with w. Then form the cross product (v × w) and take the cross product of u with that.
What is (u × v) in the diagram ?