If #A= <3, -5 ># and #B= <9, 4 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2016-03-06T06:25:45

#||A+B|| - ||A|| - ||B|| = sqrt145 - sqrt34 - sqrt97#

#||A|| = sqrt{3^2 + (-5)^2}#

#= sqrt34#

#||B|| = sqrt{9^2 + 4^2}#

#= sqrt97#

#A + B = <12,-1>#

#||A + B|| = sqrt{12^2 + 1^2}#

#= sqrt145#

#||A+B|| - ||A|| - ||B|| = sqrt145 - sqrt34 - sqrt97#