If A=<−9,2,5>, B=<−8,3,4> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Aug 15, 2017

The angle is =48.7∘

Explanation:

Let's start by calculating

→C=→A−→B

#vecC=〈-9,2,5〉-〈-8,3,4〉=〈-1,-1,1>

The angle between →A and →C is given by the dot product definition.

→A.→C=∥→A∥⋅∥→C∥cosθ

Where θ is the angle between →A and →C

The dot product is

→A.→C=⟨−9,2,5⟩.⟨−1,−1,1⟩=9−2+5=12

The modulus of →A= ∥∥⟨−9,2,5⟩∥=√81+4+25=√110

The modulus of →C= ∥∥⟨−1,−1,1⟩∥=√1+1+1=√3

So,

cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=12√110⋅√3=0.66

θ=48.7∘

Related questions
See all questions in Vectors
Impact of this question
1485 views around the world
You can reuse this answer
Creative Commons License