What is the angle between #<-2,3,1> # and #< 4,1,4 >#?

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Answer 1 · 2017-01-03T08:23:31

The answer is #=92.7#º

We use the dot product definition to calculate the angle #theta# between 2 vectors,

#veca.vecb=∥veca∥*∥vecb∥*cos theta#

#cos theta=(veca.vecb)/(∥veca∥*∥vecb∥)#

We start by calculating the dot product,

#veca:vecb=〈-2,3,1〉*〈4,1,4〉=(-8+3+4)=-1#

The modulus of #veca=∥〈-2,3,1〉∥=sqrt(4+9+1)=sqrt14#

The modulus of #vecb=∥〈4,1,4〉∥=sqrt(16+1+16)=sqrt33#

#cos theta=-1/(sqrt14*sqrt33)=-0.465#

#theta=92.7#º