If A=<5,2,−5>, B=<6,5,9> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jul 6, 2017

The angle is =56º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨5,2,−5⟩−⟨6,5,9⟩=⟨−1,−3,−14⟩

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=⟨5,2,−5⟩.⟨−1,−3,−14⟩=−5−6+70=59

The modulus of →A= ∥∥⟨5,2,−5⟩∥=√25+4+25=√54

The modulus of →C= ∥∥⟨−1,−3,−14⟩∥=√1+9+196=√206

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=59√54⋅√206=0.56

θ=56º

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