Calculating Vector Norms: Solving for Magnitude of Vectors

[kwal0203]

Homework Statement

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

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

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

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 $\sqrt{26}$

 

[HallsofIvy]

Your work is correct.

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.

 

[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 :)