What is the angle between <6,−2,9> and <−2,1,−8>?

1 Answer
Narad T.
Mar 20, 2018

The angle is =160.3∘

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=⟨6,−2,9⟩.⟨−2,1,−8⟩=−12−2−72=−86

The modulus of →A= ∥∥⟨6,−2,9⟩∥=√36+4+81=√121=11

The modulus of →B= ∥∥⟨−2,1,−8⟩∥=√4+1+64=√69

So,

cosθ=→A.→B∥∥∥→A∥⋅∥→B∥∥∥=−8611⋅√69=−0.94

θ=arccos(−0.94)=160.3∘

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