If A=<4,2,5>, B=<6,2,−7> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jan 6, 2017

The angle is 50.4º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨4,2,5⟩−⟨6,2,−7⟩=⟨−2,0,12⟩

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⟩.⟨−2,0,12⟩=−8+0+60=52

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

The modulus of →C= ∥∥⟨−2,0,12⟩∥=√4+0+144=√148

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=52√45⋅√148=0.637

θ=50.4º

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