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Finding norm of some vectors

  1. Mar 5, 2013 #1
    1. The problem statement, all variables and given/known data

    [itex]u=(2,-2,3)[/itex]
    [itex]v=(1,-3,4)[/itex]
    [itex]w=(3,6,-4)[/itex]

    1.
    [itex]\left \| 2u-4v+w \right \|[/itex]

    2.
    [itex]\left \| u \right \|-\left \| v \right \|[/itex]


    3. The attempt at a solution

    1.
    [itex]\left \| 2(2,-2,3)-4(1,-3,4)+(3,6,-4) \right \|[/itex]
    [itex]\left \| (4,-4,6)+(-4,12,-16)+(3,6,-4) \right \|[/itex]
    [itex]\left \| (3,14,-14)\right \|[/itex]

    [itex]=\sqrt{3^{2}+14^{2}+(-14)^{2}}[/itex]
    [itex]=\sqrt{9+196+196}[/itex]
    [itex]=\sqrt{401}[/itex]

    answer in book is [itex]\sqrt{529}[/itex]

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

    answer in book is [itex]\sqrt{26}[/itex]
     
  2. jcsd
  3. Mar 5, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
  4. Mar 5, 2013 #3
    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 :)
     
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