If A=<8,1,−5>, B=<6,−2,4>, and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jan 5, 2017

The answer is =45.9º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨8,1,−5⟩−⟨6,−2,4⟩=⟨2,3,−9⟩

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=⟨8,1,−5⟩.⟨2,3,−9⟩=16+3+45=64

The modulus of →A= ∥∥⟨8,1,−5⟩∥=√64+1+25=√90

The modulus of →C= ∥∥⟨2,3,−9⟩∥=√4+9+81=√94

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=64√90⋅√94=0.696

θ=45.9º

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