If A=<3,−1,5>, B=<5,2,8> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jan 24, 2017

The angle is =130.4º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨3,−1,5⟩−⟨5,2,8⟩=⟨−2,−3,−3⟩

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=⟨3,−1,5⟩.⟨−2,−3,−3⟩=−6+3−15=−18

The modulus of →A= ∥∥⟨3,−1,5⟩∥=√9+1+25=√35

The modulus of →C= ∥∥⟨−2,−3,−3⟩∥=√4+9+9=√22

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=−18√35⋅√22=−0.65

θ=130.4º

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