Thornton & Marion, Classical Dynamics, 5th Edition
Chapter 1. Matrices, Vectors, and Vector Calculus
Problem 02. Trigonometric properties of direction cosines
Solution
For Equation (1.10): Proof)
Using Figure 1-4 (a) in the book, let the length of a point P on the line from the origin be
, then
Therefore, it becomes
For Equation (1.11):
In Figure 1-4 (b) in the book, let the length of a point P on the line from the origin be
and the length of a point P’ on the line
be
.
Using the law of cosines,
Since the equation becomes
Therefore,