1) The angle that two vectors formandis considered not orientated. That is to say, is the same angle that formand: =. As consequence, the scalar product is commutative:

·= ||||cos() = ||||cos() = ·

2) What does it happen if in a scalar product we multiply one of the two vectors by one scalar r? The answer is that all the product is multiplied by the scalar r, that is to say, is verified the associativity with respect to the product for scalars:

· ( r) = r(·)
( r) ·= r(·)

To see it, fix you that:
- if r is positive, the angle that form and  r is the same that which formand;
   then · ( r) = ||| r|cos(r) = r ||||cos() = r(·)
- if r is negative, the angle that formand  rand the angle that formandare complementary;
   then cos(r) = - cos() and we can write
  · ( r) = ||| r|cos(r) = - r ||||[-cos()] = r(·)

In a similar way is proceed if r multiplies the other vector .