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

1 Answer
Jan 16, 2016

||A+B||−||A||−||B||=24.45||A+B||||A||||B||=24.45

Explanation:

  • To find the magnitude of any vector vecV=< x,y >"V=<x,y> in the standard form (its tail is at the origin), just apply the formula:
    |V|=sqrt(x^2+y^2)|V|=x2+y2
  • To find the sum of two vectors AA and BB, add the x-coordinates and the y-coordinates separately.
  • vec(A+B)=< 1,12>−−−A+B=<1,12>
  • ||A||=sqrt(2^2+6^2)=sqrt(40)||A||=22+62=40
    ||B||=sqrt((-1)^2+6^2)=sqrt(37)||B||=(1)2+62=37
    ||A+B||=sqrt(1^2+12^2)=sqrt(145)||A+B||=12+122=145
  • ||A+B||−||A||−||B||=" "sqrt(145)-sqrt(40)-sqrt(37)||A+B||||A||||B||= 1454037
    =24.45=24.45