Finding norm of some vectors

1. Mar 5, 2013

kwal0203

1. The problem statement, all variables and given/known data

$u=(2,-2,3)$
$v=(1,-3,4)$
$w=(3,6,-4)$

1.
$\left \| 2u-4v+w \right \|$

2.
$\left \| u \right \|-\left \| v \right \|$

3. The attempt at a solution

1.
$\left \| 2(2,-2,3)-4(1,-3,4)+(3,6,-4) \right \|$
$\left \| (4,-4,6)+(-4,12,-16)+(3,6,-4) \right \|$
$\left \| (3,14,-14)\right \|$

$=\sqrt{3^{2}+14^{2}+(-14)^{2}}$
$=\sqrt{9+196+196}$
$=\sqrt{401}$

answer in book is $\sqrt{529}$

2.
$\left \| (2,-2,3) \right \|-\left \| 1,-3,4 \right \|$
$\sqrt{2^{2}+(-2)^{2}+3^{2}}-\sqrt{1^{2}+(-3)^{2}+4^{2}}$
$\sqrt{4+4+9}-\sqrt{1+9+16}$
$\sqrt{17}-\sqrt{26}$

answer in book is $\sqrt{26}$

2. Mar 5, 2013

HallsofIvy

Staff Emeritus

I see three possibilities:
1) The answers in the book are wrong.
2) You have copied the problems incorrectly.
3) You have accidently copied the answers for the wrong problem.

3. Mar 5, 2013

kwal0203

Hmmm, this is strange. I knew my method was correct so I went on to the next set and still my answers are not matching the book! Thanks for your input :)