If A=<2,4,−9>, B=<3,0,−5> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Feb 25, 2017

The angle is 30º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨2,4,−9⟩−⟨3,0,−5⟩=⟨−1,4,−4⟩

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=⟨2,4,−9⟩.⟨−1,4,−4⟩=−2+16+36=50

The modulus of →A= ∥∥⟨2,4,−9⟩∥=√4+16+81=√101

The modulus of →C= ∥∥⟨−1,4,−4⟩∥=√1+16+16=√33

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=50√101⋅√33=0.866

θ=30º

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