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

1 Answer
Narad T.
Jan 23, 2017

The angle is =127º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨−6,2,1⟩−⟨−8,8,4⟩=⟨2,−6,−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=⟨−6,2,1⟩.⟨2,−6,−3⟩=−12−12−3=−27

The modulus of →A= ∥∥⟨−6,2,1⟩∥=√36+4+1=√41

The modulus of →C= ∥∥⟨2,−6,−3⟩∥=√4+36+9=√49=7

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=−27√41⋅7=−0.6

θ=127º

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