If $A= <6, -1 >$ and $B= <-3, 6>$ , what is $||A+B|| -||A|| -||B||$ ?

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Answer 1 · 2016-10-31T06:28:30

The answer is $sqrt34-sqrt37-sqrt45$

The modulus of a vector $〈x,y〉$ is $=sqrt(x^2+y^2)$

So modulus of $vecA$ is $∥〈6,-1〉∥=sqrt(36+1)=sqrt37$

So modulus of $vecB$ is $∥〈-3,6〉∥=sqrt(9+36)=sqrt45$

$〈vecA〉+〈vecB〉 =〈6,-1〉+〈-3,6〉=〈3,5〉$

So the modulus of $〈vecA〉+〈vecB〉$ is $∥〈vecA〉+〈vecB〉∥$

$=sqrt(9+25)=sqrt34$

And finally
$∥vecA+vecB∥-∥vecA∥-∥vecB∥ =sqrt34-sqrt37-sqrt45$

If A= <6, -1 >A= <6, -1 > and B= <-3, 6>B= <-3, 6>, what is ||A+B|| -||A|| -||B||||A+B|| -||A|| -||B||?