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

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