Suppose u and v are vectors in real numbers...

Question

Determine whether each statement is always true or not always true.

u dot v = v dot u

u cross v = -(v cross u)

-u dot v = -(u dot v)

-u cross -v = -(u cross v)

Answer 1

The first three are true, but

-u cross -v = (u cross v)

because the two negations cancel each other (like in multiplication between numbers).