Griffiths (3rd Edition), Chapter 01, Problem 1.1 Solution

Problem 1.1 Dot and Cross Product

$\mathbf{A} \cdot \mathbf{B} \equiv AB \cos\theta$
$\mathbf{A} \times \mathbf{B} \equiv AB \sin\theta \hat{n}$
$\mathbf{A} \cdot ( \mathbf{B} + \mathbf{C} ) = \mathbf{A} \cdot \mathbf{B} + \mathbf{A} \cdot \mathbf{C}$
$\mathbf{A} \times ( \mathbf{B} + \mathbf{C} ) = \mathbf{A} \times \mathbf{B} + \mathbf{A} \times \mathbf{C}$