If #A= <-5 ,3 ,-7 ># and #B= <2 ,2 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2017-06-21T05:35:09

The answer is #=-137.3#

The dot product is

#vecA.vecB=<-5,3,-7>.<2,2,8>#

#=-10+6-56=-60#

The magnitude of #vecA# is

#=||vecA||=||<-5,3,-7>||=sqrt((-5)^2+(3)^2+(-7)^2)#

#=sqrt(25+9+49)=sqrt83#

The magnitude of #vecB# is

#=||vecB||=||<2,2,8>||=sqrt((2)^2+(2)^2+(8)^2)#

#=sqrt(4+4+64)=sqrt72#

Therefore,

#vecA.vecB-||vecA||*||vecB||=-60-sqrt83sqrt72#

#=-137.3#