If A=<2,−5,−4>, B=<−9,1,7> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Mar 9, 2017

The angle is =30.9º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨2,−5,−4⟩−⟨−9,1,7⟩=⟨11,−6,−11⟩

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=⟨2,−5,−4⟩.⟨11,−6,−11⟩=22+30+44=96

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

The modulus of →C = ∥∥⟨11,−6,−11⟩∥=√121+36+121=√278

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=96√45⋅√278=0.86

θ=30.9º

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