If #A= <-3 ,3 ,-1 ># and #B= <8 ,7 ,6 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-12-13T16:29:39

The answer is #=-62.2#

The vectors are

#vecA= <-3,3,-1>#

#vecB = <8,7,6>#

The modulus of #vecA# is #=||vecA||=||<-3,3,-1>||=sqrt((-3)^2+(3)^2+(-1)^2)=sqrt(9+9+1)=sqrt19#

The modulus of #vecB# is #=||vecB||=||<8,7,6>||=sqrt((8)^2+(7)^2+(6)^2)=sqrt(64+49+36)=sqrt149#

Therefore,

#||vecA|| xx||vecB||=sqrt(19)*sqrt149=sqrt2831#

The dot product is

#vecA.vecB= <-3,3,-1> .<8,7,6> =(-3xx8)+(3xx7)+(-1xx6)=-24+21-6=-9#

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=-9-sqrt2831= -62.2#