If #A= <-7, 6 ># and #B= <-3, 8>#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2016-08-01T03:57:34

#||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73#

#~=-0.56#.

# A=<-7,6>, B=<-3,8>

#rArr ||A||=sqrt{(-7)^2+6^2}=sqrt(49+36)=sqrt85#, and,

#||B||=sqrt(9+64)=sqrt73#>.

#A+B=<-7-3,6+8>#=#<-10,14>#

#:. ||A+B||=sqrt(100+196)=sqrt296#.

Hence, #||A+B||-||A||-||B||=sqrt296-sqrt85-sqrt73#

#~=17.20-9.22-8.54=-0.56#.