Griffiths (3rd Edition), Chapter 01, Problem 1.4 Solution

Griffiths, Introduction to Electrodynamics, 3rd Edition Chapter 01. Vector Analysis 1.1 Vector Algebra 1.1.2 Vector Algebra: Component Form Problem 1.4 The cross product The problem asks you to find the components of the unit vector perpendicular to the plane shown in given figure. You should know about the cross product of vectors and its property….

Griffiths (3rd Edition), Chapter 01, Problem 1.3 Solution

Griffiths, Introduction to Electrodynamics, 3rd Edition Chapter 01. Vector Analysis 1.1 Vector Algebra 1.1.2 Vector Algebra: Component Form Problem 1.3 Property of the dot product The problem asks you to find the angle between the body diagonals of a cube. You should know about the dot product of vectors and its property. Solution  

Thornton & Marion (5th Edition), Chapter 01, Exercise Problem 10

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 10. Differentiation of a vector The problem asks you to calculate vector derivatives to get velocity and acceleration of a particle. The problem gives position vector of a particle in a plain elliptical orbit. We should know about calculation of…

Thornton & Marion (5th Edition), Chapter 01, Exercise Problem 09

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 09. Vector calculation The problem asks you to evaluate some vector calculation. The problem gives Two vectors 1) 2) We should know about some vector calculus, such as 1) addition and subtraction 2) dot product and cross product Solution  

Griffiths (3rd Edition), Chapter 01, Problem 1.2 Solution

Griffiths, Introduction to Electrodynamics, 3rd Edition Chapter 01. Vector Analysis 1.1 Vector Algebra Problem 1.2 Property of the cross product (associative) The problem asks you to prove whether the cross product is associative or not. You should know about the cross product of a vector and its property. Solution  

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) You should know about Distributive law of the dot and cross product. Solution  

Thornton & Marion (5th Edition), Chapter 01, Exercise Problem 07

Chapter 1. Matrices, Vectors, and Vector Calculus Problem 07. Scalar Product of two (unit) vectors The problem asks you to 1) Find the vectors describing the diagonals 2) The angle between diagonal vectors This problem assumes A unit cube in the Cartesian (Rectangular) coordinate system We should know about 1) Position vectors 2) Scalar Product…

Thornton & Marion (5th Edition), Chapter 01, Exercise Problem 06

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 06. Another proof of the orthogonality condition The problem asks you to prove that Equation (1.15) can be obtained by using the fact that the transformation matrix preserves the length of the line segment. This problem assumes that the coordinate…

Thornton & Marion (5th Edition), Chapter 01, Exercise Problem 05

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 05. The determinant of the transformation matrix The problem asks you to show that This problem assumes the transformation matrix to be a two-dimensional orthogonal matrix. You should know about 1) Calculation of a determinant 2) Properties of the orthogonal…