If #A= <-2, 2 ># and #B= <3, 4>#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2018-07-01T10:25:36

#=> color(magenta)(sqrt(37)-sqrt(8)-5 ~-1.7457#

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

#B=((3),(4))#

#A+B=((-2),(2)) +((3),(4))=((1),(6))#

#||A+B||=sqrt((-1)^2+(6)^2)=sqrt(37)#

#||A||=sqrt((-2)^2+(2)^2)=sqrt(8)#

#||B||=sqrt((3)^2+(4)^2)=sqrt(5)#

#:.||A+B|| - ||A|| - ||B|| = color(magenta)(sqrt(37)-sqrt(8)-5 ~-1.7457#