If $A= <2 , 6 >$ and $B= <-7, 4 >$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-06-01T21:22:59

It is $-3.2$ .

The norm of a vector with coordinates $v=< x, y >$ is defined as

$||v||=sqrt(x^2+y^2)$ .

Then we have

$||A+B||=||<2,6>+<-7,4>||$
$=||<-5,10>||=sqrt((-5)^2+10^2)=sqrt(125)\approx11.18$

$||A||=sqrt(2^2+6^2)=sqrt(4+36)=sqrt(40)\approx6.32$

$||B||=sqrt((-7)^2+4^2)=sqrt(49+16)=sqrt(65)\approx8.06$

Finally

$||A+B||-||A||-||B||=11.18-6.32-8.06=-3.2$ .

If A= <2 , 6 >A= <2 , 6 > and B= <-7, 4 >B= <-7, 4 >, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?