No. The two possible cross products between **u** and **v**
*point in opposite directions.*

The picture shows two vectors **u** and **v**
and the parallelogram
they define between them.

The area of the parallelogram is:
| **u** | | **v** | sin θ
where
θ
is the enclosed angle.

This area is the same as the magnitude of the cross product.
This fact is sometimes helpful in visualizing the cross product.
For example,
if **u** is rotated so that its orientation approaches that of **v**
(but its length is not changed),
the area of the parallelogram gets close to zero,
as does the magnitude of the cross product.

What angle between **u** and **v** will *maximize*
their cross product? (Hint: look at the diagram)