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Using	the	Scalar	Product	to	Prove	the	Cosine	Rule		
	
	
Part	A		
Before	we	start	this	proof	you	need	to	use	the	following	...
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Using the scalar product to prove the cosine rule

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Proving the Cosine Rule

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Using the scalar product to prove the cosine rule

  1. 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)!

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