If #A= <2 ,7 ,-4 ># and #B= <-1 ,-9, 2 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-11-28T17:57:00

The answer is #=-150.03#

The vectors are

#vecA= <2,7,-4>#

#vecB = <-1,-9,2>#

The modulus of #vecA# is #=||vecA||=||<2,7,-4>||=sqrt((2)^2+(7)^2+(-4)^2)=sqrt(4+49+16)=sqrt69#

The modulus of #vecB# is #=||vecB||=||<-1,-9,2>||=sqrt((-1)^2+(-9)^2+(2)^2)=sqrt(1+81+4)=sqrt86#

Therefore,

#||vecA|| *||vecB||=sqrt69*sqrt86=sqrt5934#

The dot product is

#vecA.vecB= <2,7,-4> .<-1,-9,2>#

# =(2xx-1)+(7xx-9)+(-4xx2)#

#=-2-63-8=-73 #

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=-73-sqrt5934= -150.03#