What is the angle between <0,9,−6> and <1,3,5>?

1 Answer
Narad T.
Dec 2, 2017

The angle is =92.7∘

Explanation:

The vectors are →A=<0,9,−6> and →B=<1,3,5>

The angle between →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=⟨0,9,−6⟩.⟨1,3,5⟩=(0×1)+(9×3)+(−6×5)=0+27−30=−3

The modulus of →A= ∥∥∥⟨0,9,−6⟩∥=√0+92+(−6)2=√81+36=√117

The modulus of →B= ∥∥⟨1,3,5⟩∥=√12+32+52=√1+9+25=√35

So,

cosθ=→A.→B∥∥∥→A∥⋅∥→B∥∥∥=−3√117⋅√35=−0.0469

θ=arccos(−0.0469)=92.7∘

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