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

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Answer 1 · 2016-11-05T10:51:12

The answer is #=65-sqrt114*sqrt122#

The dot product is #vecA.vecB=〈8,-5,-5〉.〈5,4,-9〉#
#=40-20+45=65#
The modulus of #vecA# is #∥vecA∥=sqrt(64+25+25)=sqrt114#

The modulus of #vecB# is #∥vecB∥=sqrt(25+16+81)=sqrt122#

And finally, we have #vecA.vecB-∥vecA∥*∥vecB∥=65-sqrt114*sqrt122#