What is the angle between $< - 4, - 1, 1 >$ $<-4,-1,1 >$ and $< - 6, - 1, - 4 >$ $<-6,-1,-4>$ ?

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Answer 1 · 2016-11-04T19:40:56

The angle is $=47.2º$

The angle $theta$ is given by the dot product definition
$vecu.vecv=∥vecu∥*∥vecv∥costheta$

$costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)$

The dot product $=〈-4,-1,1〉.〈-6,-1,-4〉=24+1-4=21$

The modulus are $sqrt(16+1+1)=3sqrt2$ and $sqrt(36+1+16)=sqrt53$

$costheta=21/(3sqrt2*sqrt53)=0.68$
$theta=47.2º$

What is the angle between <-4,-1,1 > <−4,−1,1><-4,-1,1 > and <-6,-1,-4> <−6,−1,−4><-6,-1,-4> ?