If A=<5,2,8>, B=<2,5,3> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Jan 30, 2017

The angle is =107.5º

Explanation:

Let's start by calculating

→C=→A−→B

→C=⟨5,2,8⟩−⟨2,5,3⟩=⟨3,−3,5⟩

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=⟨5,2,8⟩.⟨3,3,−5⟩=15+6−40=−19

The modulus of →A= ∥∥⟨5,2,8⟩∥=√25+4+64=√93

The modulus of →C= ∥∥⟨3,−3,5⟩∥=√9+9+25=√43

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=−19√93⋅√43=−0.3

θ=107.5º

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