# Thornton & Marion, Classical Dynamics, 5th Edition

## Chapter 1. Matrices, Vectors, and Vector Calculus

### Problem 07. Scalar Product of two (unit) vectors

#### The problem asks you to

- Find the vectors describing the diagonals
- The angle between diagonal vectors

#### This problem assumes

- A unit cube in the Cartesian (Rectangular) coordinate system

#### We should know about

- Position vectors
- Scalar Product of vectors

#### Solution

**1) Find diagonal vectors**

First, we can define the vector from the origin to (1,1,1). And, we can also define the vector from (0,0,1) to (1,1,0). Thus, a pair of diagonal vectors can be expressed as

**2) The angle between diagonal vectors**

From the scalar product,

Since,

Therefore,