If #A= <-2 ,3 ,3 ># and #B= <-9 ,2 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-12-05T14:31:47

The answer is #=-9.25#

The vectors are

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

#vecB = <-9,2,8>#

The modulus of #vecA# is #=||vecA||=||<-2,3,3>||=sqrt((-2)^2+(3)^2+(3)^2)=sqrt(4+9+9)=sqrt22#

The modulus of #vecB# is #=||vecB||=||<-9,2,8>||=sqrt((-9)^2+(2)^2+8^2)=sqrt(81+4+64)=sqrt149#

Therefore,

#||vecA|| xx||vecB||=sqrt(22)*sqrt149=sqrt3278#

The dot product is

#vecA.vecB= <-2,3,3> .<-9,2,8> =(-2xx-9)+(3xx2)+(3xx8)=18+6+24=48#

Therefore,

#vecA.vecB-||vecA|| xx||vecB||=48-sqrt3278= -9.25#