Distributive property of the vector dot product

If the vector dot product possesses the distributive property, then

(1)

This relationship can be proven by manipulating the left side to match the right.
Expanding the dot products:

(2)

Rearranging for a more convenient order:

(3)

Collecting the terms containing similar components of s:

(4)

Finally, by placing this in vector dot product form, equation 1 emerges.

(1)	So, since this is true, the vector dot product does possess the distributive property.