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Magnitude of Cross Product Mismatch

  1. Jan 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the magnitude of the vector product w ⃗x u, where w=<1,0,1> and u=<1,1,0>.


    2. Relevant equations

    ||w x u|| = ||w|| ||u|| sin θ


    cos θ = [itex]\frac{w.u}{||w|| ||u||}[/itex]

    3. The attempt at a solution
    w ⃗x u ⃗= -i ̂+j ̂+k ̂
    ‖||w ⃗x u|| ⃗ ‖= √3

    but

    cos⁡θ= (w ⃗∙ u ⃗)/(‖||w|| ⃗||u||) ⃗ ‖ = 1/(√2 √2) implying ⟹ θ=[itex]\pi[/itex]/4
    which then makes
    ‖||w ⃗x u|| ⃗ ‖= ‖||w|| ⃗||‖‖u|| ⃗sin⁡θ
    become
    ‖||w ⃗x u|| ⃗ ‖= √2 √2 sin⁡〖[itex]\pi[/itex]/4
    or the sqrt(2).

    What's wrong here?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 20, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    You've got cos(theta)=1/2. That doesn't show theta=pi/4. It's not. What is it?
     
  4. Jan 20, 2012 #3
    Thank you so much.
    cos theta = .5 implies that theta is pi/3 , which would make it work both ways. I can't tell you how long I have been just staring at this problem. Thanks.
     
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