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

1 Answer
Narad T.
May 22, 2017

The angle is =59.1º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨6,4,−3⟩−⟨7,−1,5⟩=⟨−1,5,−8⟩

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=⟨6,4,−3⟩.⟨−1,5,−8⟩=−6+20+24=38

The modulus of →A= ∥∥⟨6,4,−3⟩∥=√36+16+9=√61

The modulus of →C= ∥∥⟨−1,5,−8⟩∥=√1+25+64=√90

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=38√61⋅√90=0.51

θ=59.1º

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