The scalar product

Abstract

In any triangle ABC, the cosine rule states that

$${{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ab\cos \theta ,$$

((3.1))

where a, b, c are the lengths of the sides BC, CA, AB respectively and θ is the angle ACB. If a, b, c are vectors represented by the displacements $\overrightarrow{{CB}},\overrightarrow{{CA}},\overrightarrow{{AB}}$ respectively, equation (3.1) may be written in the form

$${{\left| c \right|}^{2}}={{\left| a \right|}^{2}}+{{\left| b \right|}^{2}}-2\left| a \right|\left| b \right|\cos \theta ,$$

where θ is the angle between the vectors a and b.