What is the angle between #<-5,7,6 > # and #<0,-4,8> #?

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Answer 1 · 2016-11-27T12:19:45

The angle is #=77.7#º

The angle between 2 vectors #veca# and #vecb#is given by the dot product definition

#veca.vecb=∥veca∥*vecb∥costheta#

where #theta# is the angle between the 2 vectors

Here,

#veca=〈-5,7,6〉#

#vecb=〈0,-4,8〉#

The dot product is #veca.vecb=〈-5,7,6〉.〈0,-4,8〉#

#=0-28+48=20#

The modulus of #veca=∥〈-5,7,6〉∥=sqrt(25+49+36)=sqrt110#

The modulus of #vecb=∥〈0,-4,8〉∥=sqrt(0+16+64)=sqrt80#

#costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=20/(sqrt110*sqrt80)#

#costheta=0.21#

#theta=77.7#º