What is the angle between <−7,−9,−2> and <2,−3,5>?

1 Answer
Narad T.
Dec 14, 2016

The angle is =87.7º

Explanation:

The angle between 2 vectors is given by the dot product definition

→a.→b=∥→a∥⋅∥→b∥⋅cosθ

The dot product is

⟨−7,−9,−2⟩.⟨2,−3,5⟩=((−7⋅2)+(−9⋅−3)+(−2⋅5))

=−14+27−10=3

The modulus of →a=∥⟨−7,−9,−2⟩∥=√63+81+4=√144=12

The modulus of →b=∥⟨2,−3,5⟩∥=√4+9+25=√38

Therefore,

cosθ=→a.→b∥∥∥→a∥⋅∥→b∥∥∥=312√38=0.04

θ=87.7º

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