If #A= <5 , 6 ># and #B= <-1,7 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2017-06-16T06:29:58

The answer is #=-1.28#

The vectors are

#vecA=<5,6>#

#vecB=<-1,7>#

#vecA+vecB=<5,6> + <-1,7> =<4,13>#

The modulus of #vecA# is

#||vecA|| = ||<5,6>||=sqrt(5^2+6^2)=sqrt(25+36)=sqrt61#

The modulus of #vecB# is

#||vecB|| = ||<-1,7>||=sqrt((-1)^2+7^2)=sqrt(1+49)=sqrt50#

The modulus of #(vecA+vecB)# is

#||vecA+vecB||=||<4,13>||=sqrt(4^2+13^2)=sqrt(16+169)=sqrt185#

Therefore,

#||vecA+vecB||-||vecA||-||vecB||=sqrt185-sqrt61-sqrt50=-1.28#