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

1 Answer
Narad T.
Mar 14, 2018

The angle is =36.1∘

Explanation:

Start by calculating

→C=→A−→B

→C=⟨7,−5,4⟩−⟨4,7,−3⟩=⟨3,−12,7⟩

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,−5,4⟩.⟨3,−12,7⟩=21+60+28=109

The modulus of →A= ∥∥⟨7,−5,4⟩∥=√49+25+16=√90

The modulus of →C= ∥∥⟨3,−12,7⟩∥=√9+144+49=√202

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=109√90⋅√202=0.81

θ=arccos(0.81)=36.1∘

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