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#