If A=<6,8,2>, B=<7,1,−4> and C=A−B, what is the angle between A and C?

1 Answer
Narad T.
Nov 22, 2016

THe angle is 49º

Explanation:

Let's start by calculating →C

→C=→A−→B=⟨6,8,2⟩−⟨7,1,−4⟩=⟨−1,7,6⟩

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

→A.→C=∥→A∥⋅∥→C∥⋅cosθ

where, θ is the angle between the two vectors.

The dot product is
=⟨−1,7,6⟩.⟨6,8,2⟩=−6+56+12=62

The modulus of →A is

∥∥∥→A∥=∥⟨6,8,2⟩∥=√36+64+4=√104

The modulus of →C is

∥∥∥→C∥=∥⟨−1,7,6⟩∥=√1+49+36=√86

Therefore,
cosθ=→A.→C∥∥∥→A∥⋅∥→C∥∥∥=62√104⋅√86=0.66

θ=49º

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