What is the angle between #<4,7,1 ># and #<9,5,4> #?

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Answer 1 · 2016-11-12T19:21:25

The angle is #=33.3#º

Let the angle be #theta#

Let #vecu=〈4,7,1〉#

and #vecv=〈9,5,4〉#

The angle is given by the dot product definition

#vecu.vecv=∥vecu∥*∥vecv∥costheta#

#vecu.vecv=〈4,7,1〉.〈9,5,4〉=36+35+4=75#

#∥vecu∥=∥〈4,7,1〉∥=sqrt(16+49+1)=sqrt66#

#∥vecv∥=∥〈9,5,4〉∥=sqrt(81+25+16)=sqrt122#

Therefore, #costheta=75/(sqrt66*sqrt122)=0.84#

#theta=33.3#º