How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = - 2j -5k and B = - 4i + j - 4k?

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Answer 1 · 2017-06-03T12:14:41

The angle is $=54.4º$

The dot product or scalar product of 2 vectors, $vecA$ and $vecB$ is

$vecA.vecB=||vecA||*||vecB||*cos theta$

Where $theta$ is the angle between the 2 vectors

$costheta=(vecA.vecB)/(||vecA||*||vecB||)$

The dot product is $=vecA.vecB=<0,-2,-5>.<-4,1,-4>$

$=(0*-4)+(-2*1)+(-5*-4)$

$=0-2+20=18$

The magnitude of $vecA$ is $=||<0,-2,-5>||=sqrt(0+4+25)=sqrt29$

The magnitude of $vecB$ is $=||<-4,1,-4>||=sqrt(16+1+16)=sqrt33$

$cos theta=18/(sqrt29*sqrt33)=0.58$

$theta=54.4º$