## 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 of vectors

##### Solution

1) Find diagonal vectorsFirst, 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 as2) The angle between diagonal vectorsFrom the scalar product,Since, Therefore,