Properties of Dot Product

Another property of the dot product is:

(au + bv) • w = (au) • w + (bv) • w, where a and b are scalars

Here is the list of properties of the dot product:

1. u • v = |u||v| cos θ
2. u • v = v • u
3. u • v = 0 when u and v are orthogonal.
4. 0 • 0 = 0
5. |v|² = v • v
6. a (u•v) = (a u) • v
7. (au + bv) • w = (au) • w + (bv) • w