If #A= <8 ,- 2 ,9># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-06-03T13:49:31

The result is #=-183.9#

The dot product is

#vecA.vecB=<8,-2.9>.<5,4,-9> =(8*5)+(-2*4)+(9*-9)#

#=40-8-81=-49#

The modulus of #vecA# is

#||vecA||=||<8,-2,9>||=sqrt(64+4+81)=sqrt149#

The modulus of #vecB# is

#||vecB||=||<5,4,-9>||=sqrt(25+16+81)=sqrt122#

Therefore,

#vecA.vecB-||vecA||+||vecB||#

#=-49-sqrt(149*122)#

#=-183.8#