If A=<6,−7,8>, B=<1,−5,−2> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jan 8, 2017

The angle is =26.6º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨6,−7,8⟩−⟨1,−5,−2⟩=⟨5,−2,10⟩

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=⟨6,−7,8⟩.⟨5,−2,10⟩=30+14+80=124

The modulus of →A= ∥∥⟨6,−7,8⟩∥=√36+49+64=√149

The modulus of →C= ∥∥⟨5,−2,10⟩∥=√25+4+100=√129

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=124√149⋅√129=0.894

θ=26.6º

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