What is the angle between <−5,−3,6> and <3,9,−9>?

1 Answer
Narad T.
Mar 19, 2018

The angle is =151.3∘

Explanation:

The angle between 2 vectors, →A and →B is given by the dot product definition.

→A.→B=∥→A∥⋅∥→B∥cosθ

Where θ is the angle between →A and →B

The dot product is

→A.→B=⟨−5,−3,6⟩.⟨3,9,−9⟩=−15−27−54=−96

The modulus of →A= ∥∥⟨−5,−3,6⟩∥=√25+9+36=√70

The modulus of →B= ∥∥⟨3,9,−9⟩∥=√9+81+81=√171

So,

cosθ=→A.→B∥∥∥→A∥⋅∥→B∥∥∥=−96√70⋅√171=−0.877

θ=arccos(−0.877)=151.3∘

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