## Chapter 01. 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 , thenTherefore, it becomes

For Equation (1.11): Proof) 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,

##### Reference

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