If #A= <-3, 6 ># and #B= <-2, 5 >#, what is #||A+B|| -||A|| -||B||#?

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Answer 1 · 2017-12-16T09:30:04

The answer is #=-0.01#

The vectors are

#vecA= <-3,6>#

#vecB = <-2,5>#

The modulus of #vecA# is #=||vecA||=||<-3,6>||=sqrt((-3)^2+(6)^2)=sqrt(9+36)=sqrt45#

The modulus of #vecB# is #=||vecB||=||<-2,5>||=sqrt((-2)^2+(5)^2)=sqrt(4+25)=sqrt29#

The modulus of #(vecA+vecB)# is

#||vecA+vecB||= ||<-3,6,> +<-2,5>|| =||< -5,11>||#

#=sqrt((-5)^2+11^2)#

#=sqrt(25+121)#

#=sqrt146#

Therefore,

#||vecA+vecB||-||vecA|| -||vecB||=sqrt(146)-sqrt(45)-sqrt(29)= -0.01#