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

1 Answer
Narad T.
Oct 31, 2016

The answer is #sqrt34-sqrt37-sqrt45#

Explanation:

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#

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