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 :)