If A=<7,9,4>, B=<4,6,−3> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Nov 14, 2017

The angle is =39.8∘

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨7,9,4⟩−⟨4,6,−3⟩=⟨3,3,7⟩

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=⟨7,9,4⟩.⟨3,3,7⟩=21+27+28=76

The modulus of →A= ∥∥⟨7,9,4⟩∥=√49+81+16=√146

The modulus of →C= ∥∥⟨3,3,7⟩∥=√9+9+49=√67

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=76√146⋅√67=0.77

θ=39.8∘

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