Properties of vector product

a and b are vectors

1. Vector product is not commutative

a×b ≠ b×a


a×b = - b×a

2. m is a scalar
ma×b = m(a×b) = a×mb

3. m and n are scalars
ma×nb = mn(a×b) = m(a×nb) = n(ma×b)

4. Distributive property over vector addition
a×(b+c) = a×b + a×c (left distributivity)
(b+c) ×a = b×a + c×a (right distributivity)

5. a×(b-c) = a×b - a×c (left distributivity)
(b-c) ×a = b×a - c×a (right distributivity)

6. The vector product of two non-zero vectors is zero is they are parallel or collinear