Griffiths (4th Edition), Chapter 01, Problem 1.1 Solution

Griffiths, Introduction to Electrodynamics, 4th Edition

Chapter 1. Vector Analysis

Section 1. 1. Vector Algebra

1.1.1 Vector Operations

Problem 1.1 Dot and Cross Product

The problem asks you to
  • prove the dot and cross product are distributive.
This problem gives (or assumes)
  • \mathbf{A} \cdot \mathbf{B} \equiv AB \cos\theta
  • \mathbf{A} \times \mathbf{B} \equiv AB \sin\theta \hat{n}
You should know about
  • 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}
Solution

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