If A=<4,2,5>, B=<6,2,−5> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Feb 25, 2017

The angle is =52.1º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨4,2,5⟩−⟨6,2,−5⟩=⟨−2,0,10⟩

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=⟨4,2,5⟩.⟨−2,0,10⟩=−8+0+50=42

The modulus of →A= ∥∥⟨4,2,5⟩∥=√16+4+25=√45

The modulus of →C= ∥∥⟨−2,0,10⟩∥=√4+0+100=√104

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=42√45⋅√104=0.61

θ=52.1º

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