Griffiths, Introduction to Electrodynamics, 4th Edition

Chapter 1. Vector Analysis

Problem 1.1 Dot and Cross Product

• $\mathbf{A} \cdot \mathbf{B} \equiv AB \cos\theta$
• $\mathbf{A} \times \mathbf{B} \equiv AB \sin\theta \hat{n}$
• Distributive law of the dot and cross product. $\mathbf{A} \cdot ( \mathbf{B} + \mathbf{C} ) = \mathbf{A} \cdot \mathbf{B} + \mathbf{A} \cdot \mathbf{C}$ $\mathbf{A} \times ( \mathbf{B} + \mathbf{C} ) = \mathbf{A} \times \mathbf{B} + \mathbf{A} \times \mathbf{C}$