Thornton & Marion, Classical Dynamics of Particles and Systems, 5th Edition

Chapter 1. Matrices, Vectors, and Vector Calculus

Problem 19. Vector Algebra

The problem asks you to derive

1. Angle transformation formulae using vector algebra.

You should know about

1. The basic concept of a vector algebra
2. Law of cosines
3. Pythagorean trigonometric identity

Solution

References

https://en.wikipedia.org/wiki/Law_of_cosines
https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity