If #A= <2 ,8 ,-4 ># and #B= <3 ,2 ,7 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-05-31T08:36:38

The result is #=-78.17#

The dot product is

#vecA.vecB=<2,8,-4>:<3,2,7>=2*3+8*2-4*7#

#=6+16-28=-6#

The modulus of #vecA# is

#=||vecA||=||<2,8,-4>||#

#=sqrt(4+64+16)#

#=sqrt(84)#

The modulus of #vecB# is

#=||vecB||=||<3,2,7>||#

#=sqrt(9+4+49)#

#=sqrt(62)#

So,

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

#=-6-sqrt84*sqrt62#

#=-6-72.17#

#=-78.17#