Griffiths, Introduction to Electrodynamics, 4th Edition

Chapter 01. 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)

• $latex \\mathbf{A} \\cdot \\mathbf{B} \\equiv AB \\cos\\theta $
• $latex \\mathbf{A} \\times \\mathbf{B} \\equiv AB \\sin\\theta \\hat{n} $

You should know about

• Distributive law of the dot and cross product. $latex \\mathbf{A} \\cdot ( \\mathbf{B} + \\mathbf{C} ) = \\mathbf{A} \\cdot \\mathbf{B} + \\mathbf{A} \\cdot \\mathbf{C} $ $latex \\mathbf{A} \\times ( \\mathbf{B} + \\mathbf{C} ) = \\mathbf{A} \\times \\mathbf{B} + \\mathbf{A} \\times \\mathbf{C} $

Solution