If #A= <2 ,-3 ,-3 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-07-18T09:23:17

The answer is #=-81.4#

The vectors are

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

#vecB=<-2,5,7>#

The dot product is

#vecA.vecB=<2,-3,-3>.<-2,5,7>=-4-15-21=-40#

The modulus of #vecA# is

#=||<2,-3,-3>||=sqrt(4+9+9)=sqrt22#

The modulus of #vecB# is

#=||<-2,5,7>||=sqrt(4+25+49)=sqrt78#

Therefore,

#vecA.vecB-||vecA||*||vecB||#

#=-40-sqrt22*sqrt78#

#=-81.4#