If A=<4,−9,2>, B=<1,−3,−8> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Aug 3, 2017

The angle is =44.7∘

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨4,−9,2⟩−⟨1,−3,−8⟩=⟨3,−6,10⟩

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=⟨4,−9,2⟩.⟨3,−6,10⟩=12+54+20=86

The modulus of →A= ∥∥⟨4,−9,2⟩∥=√16+81+4=√101

The modulus of →C= ∥∥⟨3,−6,10⟩∥=√9+36+100=√145

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=86√101⋅√145=0.74

θ=44.7∘

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