I hope this is the right forum.

$\displaystyle u=<1,1,1>, v=<-1,2.1>$

The magnitudes are:

$\displaystyle ||u+v||=\sqrt{13}$ and

$\displaystyle ||u|| + ||v|| = \sqrt{3} + \sqrt{6}$

But the answer in the back of the book is showing $\displaystyle \sqrt{13}$ for both? Where am I going wrong?

I agree with your answers. Moreover, in a euclidean space, $\displaystyle \|u+v\| = \|u\|+\|v\|$ iff u and v are proportional, which is not the case here. There is probably a typo in the book.

Originally Posted by M.R
But the answer in the back of the book is showing $\displaystyle \sqrt{13}$ for both? Where am I going wrong?
I think you are correct, assuming I am reading your work correctly.

$\displaystyle \mathbf u = \langle1,1,1\rangle, \mathbf v = \langle-1,2,1\rangle$

$\displaystyle \|\mathbf u + \mathbf v\| = \|\langle0,3,2\rangle\| = \sqrt{13}$

$\displaystyle \|\mathbf u\| + \|\mathbf v\| = \sqrt3 + \sqrt6$

$\displaystyle \sqrt{13}\neq\sqrt3+\sqrt6$

Thank you both for the verification.

BTW, where is the thanks button?