If A=<4,1,8>, B=<5,7,3> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Mar 31, 2018

The angle is =65.0∘

Explanation:

Start by calculating

→C=→A−→B

→C=⟨4,1,8⟩−⟨5,7,3⟩=⟨−1,−6,5⟩

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=⟨4,1,8⟩.⟨−1,−6,5⟩=−4−6+40=30

The modulus of →A= ∥∥⟨4,1,8⟩∥=√16+1+64=√81=9

The modulus of →C= ∥∥⟨−1,−6,5⟩∥=√1+36+25=√62

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=309⋅√62=0.42

θ=arccos(0.42)=65.0∘

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