What is the angle between <8,−1,2> and <−4,−1,3>?

1 Answer
Narad T.
Jan 16, 2017

The angle is =53.8º

Explanation:

The angle is given by the dot product definition

→a.→b=∥→a∥⋅∥→b∥cosθ

Where, θ is the angle between the 2 vectors

Here, we have

→a=⟨8,−1,2⟩

→b=⟨−4,−1,3⟩

The dot product is ⟨8,−1,2⟩.⟨−4,−1,3⟩=−32+1+6=25

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

The modulus of →b is =∥⟨−4,−1,3⟩∥=√16+1+9=√26

Therefore,

cosθ=→a.→b∥∥∥→a∥⋅∥→b∥∥∥=25√69⋅√26=0.59

θ=53.8º

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