What is the angle between #<-7,-9,-2># and #< 2,-3,5>#?

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Answer 1 · 2016-12-14T06:22:43

The angle is #=87.7#º

The angle between 2 vectors is given by the dot product definition

#veca.vecb=∥veca∥*∥vecb∥*costheta#

The dot product is

#〈-7,-9,-2〉.〈2,-3,5〉=((-7*2)+(-9*-3)+(-2*5))#

#=-14+27-10=3#

The modulus of #veca=∥〈-7,-9,-2〉∥=sqrt(63+81+4)=sqrt144=12#

The modulus of #vecb=∥〈2,-3,5〉∥=sqrt(4+9+25)=sqrt38#

Therefore,

#costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=3/(12sqrt38)=0.04#

#theta=87.7#º