If A=<5,6,−3>, B=<−9,6,−2> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Aug 1, 2017

The angle is =51.6∘

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨5,6,−3⟩−⟨−9,6,−2⟩=⟨14,0,−1⟩

The angle between →A and →C is given by the dot product definition.

→A.→C=∥→A∥⋅∥→C∥cosθ

Where θ is the angle between →A and →C

The dot product is

→A.→C=⟨5,6,−3⟩.⟨14,0,−1⟩=70+0+3=73

The modulus of →A= ∥∥⟨5,6,−3⟩∥=√25+36+9=√70

The modulus of →C= ∥∥⟨14,0,−1⟩∥=√196+0+1=√197

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=73√70⋅√197=0.62

θ=51.6∘

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