Chapter 9 - Section 9.2 - The Dot Product - 9.2 Exercises - Page 646: 39

$u \cdot v=v \cdot u$

Let $u=\lt p_1,p_2 \gt ; v=\lt q_1,q_2 \gt$ Consider LHS $u \cdot v=(p_1)(q_1)+(p_2) (q_2)=p_1 q_1+p_2 q_2$ Next, consider RHS $v \cdot u=(q_1)(p_1)+(q_2)(p_2)=q_1p_1+q_2p_2=p_1 q_1+p_2 q_2$ Hence, $u \cdot v=v \cdot u$