If A=<−7,1,5>, B=<3,6,−2> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jun 18, 2017

The angle is =28.9º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨−7,1,5⟩−⟨3,6,−2⟩=⟨−10,−5,7⟩

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=⟨−7,1,5⟩.⟨−10,−5,7⟩=70−5+35=100

The modulus of →A= ∥∥⟨−7,1,5⟩∥=√49+1+25=√75

The modulus of →C= ∥∥⟨−10,−5,7⟩∥=√100+25+49=√174

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=100√75⋅√174=0.88

θ=28.9º

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