If #A= <2 ,6 ,-3 ># and #B= <-8 ,2 ,7 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-11-25T07:24:55

The answer is #=-100.7#

The vectors are

#vecA= <2,6,-3>#

#vecB = <-8,2,7>#

The modulus of #vecA# is #=||vecA||=||<2,6,-3>||=sqrt(2^2+(6)^2+(-3)^2)=sqrt(4+36+9)=sqrt49=7#

The modulus of #vecB# is #=||vecB||=||<-8,2,7>||=sqrt((-8)^2+^2(2)^2+)=sqrt(64+4+49)=sqrt117#

Therefore,

#||vecA|| xx||vecB||=7*sqrt117=7sqrt117#

The dot product is

#vecA.vecB= <2,6,-3> .<-8,2,7> =(2xx-8)+(6xx2)+(-3xx7)=-16+12-21=-25 #

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=-25-7sqrt117= -100.7#