If #A= <2 , 6 ># and #B= <-1,6 >#, what is #||A+B|| -||A|| -||B||#?

1 Answer
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Jan 16, 2016

#||A+B||−||A||−||B||=24.45#

Explanation:

  • To find the magnitude of any vector #vecV=< x,y >"# in the standard form (its tail is at the origin), just apply the formula:
    #|V|=sqrt(x^2+y^2)#
  • To find the sum of two vectors #A# and #B#, add the x-coordinates and the y-coordinates separately.
  • #vec(A+B)=< 1,12>#
  • #||A||=sqrt(2^2+6^2)=sqrt(40)#
    #||B||=sqrt((-1)^2+6^2)=sqrt(37)#
    #||A+B||=sqrt(1^2+12^2)=sqrt(145)#
  • #||A+B||−||A||−||B||=" "sqrt(145)-sqrt(40)-sqrt(37)#
    #=24.45#
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