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

Griffiths, Introduction to Electrodynamics, 3rd Edition

Chapter 01. Vector Analysis

1.1 Vector Algebra

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} 


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