If #A= <-2 ,-7 ,-1 ># and #B= <3 ,4 ,-8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-12-14T07:14:12

The answer is #=-95.3#

The vectors are

#vecA= <-2,-7,-1>#

#vecB = <3,4,-8>#

The modulus of #vecA# is #=||vecA||=||<-2,-7,-1>||=sqrt((-2)^2+(-7)^2+(-1)^2)=sqrt(4+49+1)=sqrt54#

The modulus of #vecB# is #=||vecB||=||<3,4,-8>||=sqrt((3)^2+(4)^2+(-8)^2)=sqrt(9+16+64)=sqrt89#

Therefore,

#||vecA|| xx||vecB||=sqrt(54)*sqrt89=sqrt4806#

The dot product is

#vecA.vecB= <-2,-7,-1> .<3,4,-8> =(-2xx3)+(-7xx4)+(-1xx-8)=-6-28+8=-26#

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=-26-sqrt4806= -95.3#