If #A= <6 ,-5 ,3 ># and #B= <-7 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-12-17T06:35:39

The answer is #=-190.1#

The vectors are

#vecA= <6,-5,3>#

#vecB = <-7,4,-9>#

The modulus of #vecA# is #=||vecA||=||<6,-5,3>||=sqrt((6)^2+(-5)^2+(3)^2)=sqrt(36+25+9)=sqrt70#

The modulus of #vecB# is #=||vecB||=||<-7,4,-9>||=sqrt((-7)^2+(4)^2+(-9)^2)=sqrt(49+16+81)=sqrt146#

Therefore,

#||vecA|| *||vecB||=sqrt(70)*sqrt146=sqrt10220#

The dot product is

#vecA.vecB= <6,-5,3> .<-7,4,-9> =(6xx-7)+(-5xx4)+(3xx-9)=-42-20-27=-89#

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=-89-sqrt10220= -190.1#