If #A= <-3, -1 ># and #B= <4, 5 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2018-07-01T10:30:04

#||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423#

#A=((-3),(-1))#

#B=((4),(5))#

#A+B=((-3),(-1)) +((4),(5))=((1),(4))#

#||A+B||=sqrt((1)^2+(4)^2)=sqrt(17)#

#||A||=sqrt((-3)^2+(-1)^2)=sqrt(10)#

#||B||=sqrt((4)^2+(5)^2)=sqrt(41)#

#:.||A+B|| - ||A|| - ||B|| = color(crimson)(sqrt(17)-sqrt(10)- sqrt(41) ~~ - 5.4423#