If #A= <3, -1 ># and #B= <9, 4 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2017-11-21T09:32:15

The answer is #=-0.64#

The vectors are

#vecA= <3,-1>#

#vecB = <9,4>#

The modulus of #vecA# is #=||vecA||=||<3,-1>||=sqrt(3^2+(-1)^2)=sqrt(9+1)=sqrt10#

The modulus of #vecB# is #=||vecB||=||<9,4>||=sqrt(9^2+(4)^2)=sqrt(81+16)=sqrt97#

#vecA+vecB= <3,-1> + <9,4> = <12,3>#

The modulus of #vecA+ vecB# is #=||vecA+ vecB||=||<12,3>||=sqrt(12^2+(3)^2)=sqrt(144+9)=sqrt153#

Therefore,

#||vecA + vecB||-||vecA|| -||vecB||=sqrt153-sqrt10-sqrt97= -0.64#