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Find unit vector and cross product

  1. Aug 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Given the two vectors written in component-unit vector form below:
    [tex]D = 3\hat{i} - \hat{j}[/tex]
    [tex]E = 2\hat{i} + 4\hat{j}[/tex]
    a.) Find the unit vector in the same direction as D
    b.) Find the cross product of D x E
    c.) Write the vector D in magnitude direction form

    2. Relevant equations



    3. The attempt at a solution
    a.)
    [tex]\hat{u} = \frac{\vec{D}}{D}[/tex]
    [tex]\hat{u} = \frac{3\hat{i}}{10} - \frac{\hat{j}}{10}[/tex]



    b.) Cz = DxEy - DyEx
    Cz = [3][4] - [-1][2]
    = 12 + 2
    = 14

    c.) D = sqrt(3^2 + 1)
    = 3.2
    theta = tan^-1(1/-3)
    = 18.4
    3.2.... 18.4 degrees S of W
     
  2. jcsd
  3. Aug 9, 2007 #2

    learningphysics

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    The denominators are wrong.

    Yes, that's correct. I'd write the final answer as [tex]14\hat{k}[/tex]

    The direction isn't right.
     
  4. Aug 9, 2007 #3
    a.) [tex]\hat{u} = \frac{10}{3\hat{i}} - \frac{10}{\hat{j}}[/tex]

    c.) D = 3.2, 18.4 S of W
    ?
     
  5. Aug 9, 2007 #4

    learningphysics

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    No, what you had before was right except that you needed sqrt(10) instead of 10 in the denominator.

    I get the direction as 18.4 S of E
     
  6. Aug 9, 2007 #5
    oh yeah i thot west is to the right
    thanks
     
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