If A=<3,−1,−7>, B=<5,6,−4> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
May 23, 2017

The angle is =68.7º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨3,−1,−7⟩−⟨5,6,−4⟩=⟨−2,−7,−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,−7⟩.⟨−2,−7,−3⟩=−6+7+21=22

The modulus of →A= ∥∥⟨3,−1,−7⟩∥=√9+1+49=√59

The modulus of →C= ∥∥⟨−2,−7,−3⟩∥=√4+49+9=√62

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=22√59⋅√62=0.36

θ=68.7º

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