If #A= <2 , 6 ># and #B= <-7, 4 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2016-06-01T21:22:59

It is #-3.2#.

The norm of a vector with coordinates #v=< x, y ># is defined as

#||v||=sqrt(x^2+y^2)#.

Then we have

#||A+B||=||<2,6>+<-7,4>||#
#=||<-5,10>||=sqrt((-5)^2+10^2)=sqrt(125)\approx11.18#

#||A||=sqrt(2^2+6^2)=sqrt(4+36)=sqrt(40)\approx6.32#

#||B||=sqrt((-7)^2+4^2)=sqrt(49+16)=sqrt(65)\approx8.06#

Finally

#||A+B||-||A||-||B||=11.18-6.32-8.06=-3.2#.