Proving the Cosine Rule

1. Using the Scalar Product to Prove the Cosine Rule
Part A
Before we start this proof you need to use the following properties of the scalar
product:
1. 𝒄 ∙ 𝒄 =
2. 𝒃 ∙ 𝒄 =
3. 𝒃 − 𝒄 ∙ (𝒃 − 𝒄) =
Part B
Label the following triangle ABC where:
𝐴𝐵 represents the vector 𝒄
𝐴𝐶 represents the vector 𝒃
What is 𝐵𝐶 in terms of 𝒄 and 𝒃? Label this on the diagram
What is 𝐵𝐶 ∙ 𝐵𝐶 ?
Using 1,2 and 3 from part A put this altogether to find the length of (𝐵𝐶)!