If #A= <-9, 2 ># and #B= <-3, 8>#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2017-12-09T15:28:47

See below.

#A=((-9),(2))#

#B=((-3),(8))#

#A+B=((-9),(2)) +((-3),(8))=((-12),(10))#

#||A+B||=sqrt((-12)^2+(10)^2)=sqrt(244)=2sqrt(61)#

#||A||=sqrt((-9)^2+(2)^2)=sqrt(85)#

#||B||=sqrt((-3)^2+(8)^2)=sqrt(73)#

#:.#

#2sqrt(61)-sqrt(85)-sqrt(73)=-2.143048852#