What is the angle between #<-4,-1,1 > # and #<-6,-1,-4> #?

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Answer 1 · 2016-11-04T19:40:56

The angle is #=47.2º#

The angle #theta# is given by the dot product definition
#vecu.vecv=∥vecu∥*∥vecv∥costheta#

#costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)#

The dot product #=〈-4,-1,1〉.〈-6,-1,-4〉=24+1-4=21#

The modulus are #sqrt(16+1+1)=3sqrt2# and #sqrt(36+1+16)=sqrt53#

#costheta=21/(3sqrt2*sqrt53)=0.68#
#theta=47.2º#