What is the angle between <−2,7,−1> and <6,−1,4>?

1 Answer
Narad T.
Feb 9, 2017

The angle is =115.5º

Explanation:

The angle between →u and →v is given by the dot product definition.

→u.→v=∥→u∥⋅∥→v∥cosθ

Where θ is the angle between →u and →v

The dot product is

→u.→v=⟨−2,7,−1⟩.⟨6,−1,4⟩=−12−7−4=−23

The modulus of →u= ∥∥⟨−2,7,−1⟩∥=√4+49+1=√54

The modulus of →v= ∥∥⟨6,−1,4⟩∥=√36+1+16=√53

So,

cosθ=→u.→v∥∥→u∥⋅∥→v∥∥=−23√54⋅√53=−0.43

θ=115.5º

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