If A=<2,−5,−8>, B=<−9,4,−2> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Nov 12, 2016

The angle is 56.1º

Explanation:

Let's calculate →C=→A−→B=⟨2,−5,−8⟩−⟨−9,4,−2⟩∘
=⟨11,−9,−6⟩

To calculate the angle θ between the 2 vectors, we use the dot product definition.

→A.→C=∥→A∥⋅∥→C∥⋅cosθ

The dot product is →A.→C=⟨2,−5,−8⟩.⟨11,−9,−2⟩
=22+45+16=83

The modulus of →A = ∥∥∥→A∥=∥⟨2,−5,−8⟩∥=√4+25+64=√93

The modulus of →C = ∥∥∥→C∥=∥⟨11,−9,−6⟩∥=√121+81+36=√238

cosθ=83√93⋅√238=0.56

θ=56.1º

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