If A = <5 ,4 ,3 >A=<5,4,3>, B = <2 ,-7 ,5 >B=<2,−7,5> and C=A-BC=A−B, what is the angle between A and C?

1 Answer
Narad T.
Nov 12, 2016

The angle is 49.649.6º

Explanation:

Let's start by calculating vecC=vecA-vecB=〈5,4,3〉-〈2,-7,5〉→C=→A−→B=⟨5,4,3⟩−⟨2,−7,5⟩

vecC=〈3,11,-2〉→C=⟨3,11,−2⟩

To calculate the angle, we use the dot productt definition,

vecA.vecC=∥〈5,4,3〉∥*∥〈3,11,-2〉∥*costheta→A.→C=∥⟨5,4,3⟩∥⋅∥⟨3,11,−2⟩∥⋅cosθ
where thetaθ is the angle between the 2 vectors

vecA.vecC=〈5,4,3〉.〈3,11,-2〉=15+44-6=53→A.→C=⟨5,4,3⟩.⟨3,11,−2⟩=15+44−6=53

Modulus of vecA=∥〈5,4,3〉∥=sqrt(25+16+9)=sqrt50→A=∥⟨5,4,3⟩∥=√25+16+9=√50

Modulus of vecC=∥〈3,11,-2〉∥=sqrt(9+121+4)=sqrt134→C=∥⟨3,11,−2⟩∥=√9+121+4=√134

:. cos theta=53/(sqrt50*sqrt134=0.65

theta=49.6º

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