What is the angle between #<-7,0 ,4> # and #< -1,5,0>#?

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Answer 1 · 2017-01-16T17:42:04

The angle is #80.2#º

The angle is given by the dot product definition

#veca.vecb=∥veca∥*∥vecb∥costheta#

Where, #theta# is the angle between the 2 vectors
Here, we have

#veca=〈-7,0,4〉#

#vecb=〈-1,5,0〉#

The dot product is #〈-7,0,4〉.〈-1,5,0〉=7+0+0=7#

The modulus of #veca# is #=∥〈-7,0,4〉∥=sqrt(49+0+16)=sqrt65#

The modulus of #vecb# is #=∥〈-1,5,0〉∥=sqrt(1+25+0)=sqrt26#

Therefore,

#costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=7/(sqrt65*sqrt26)=0.17#

#theta=80.2#º