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Vector product

  1. Jun 21, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the vector product [tex]\vec{A} \times \vec{B}[/tex] (expressed in unit vectors ) of the two vectors given. What is the magnitude of the vector product?
    [tex]\vec{A} = 5.00\hat{i} + 2.00\hat{j}[/tex]
    [tex]\vec{B} = 3.00\hat{i} - 1.00\hat{j}[/tex]


    2. Relevant equations
    [tex]\vec{A}\vec{B}\sin(\theta)[/tex]



    3. The attempt at a solution

    using pythagorean theorem i found that the resultant of the two is
    5.39 and 3.16

    plus the total angle w/c is 40.2

    using the formula mentioned above i found the answer as 11k and magnitude of 11.0

    what i am confused is that it has a different answer from the back of my book w/c is -[tex]-17\hat{k},17.0[/tex]
    who is wrong the book or me???
    and pls show me why?
     
    Last edited: Jun 21, 2007
  2. jcsd
  3. Jun 21, 2007 #2

    Doc Al

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    Staff: Mentor

    Your answer seems correct to me. As a double check, find the cross product by multiplying the components.
     
  4. Jun 21, 2007 #3
    my answer is wrong
    the unit vectors should be
    using the determinant rule
    z =AxBy - AyBy
    z = 5(-1)-2(3)

    z = -11

    -11\hat{k}

    and the magnitude is where u use ABsin(theta) =11.0
     
  5. Jun 21, 2007 #4

    Doc Al

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    Why do you say your answer is wrong? (Note that both methods gave you the same answer.)
     
  6. Jun 21, 2007 #5
    :confused:
    how?

    ...
    the components shud be positive??
    now im confused
     
    Last edited: Jun 21, 2007
  7. Jun 21, 2007 #6

    Doc Al

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    I'm not sure what you are asking. In your first post, you showed how you arrived at your solution. (Yes, your sign was wrong, but all you needed was the magnitude.) I said it was correct and asked you to double-check using a different method. You did and got the same answer for the magnitude. So why do you think your answer is wrong?
     
  8. Jun 21, 2007 #7
    i thought this has two questions
    Finding vector product AXB expressed in unit vectors and magnitude
     
  9. Jun 21, 2007 #8

    D H

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    Staff Emeritus
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    Are you sure that you have both vectors stated properly? For example, flipping the x and y components of B yields the answer in the book: [tex]\vec B = 1.00\hat i - 3.00\hat j[/tex]. This is an easy mistake to make -- either by you or by the authors.
     
  10. Jun 21, 2007 #9

    Doc Al

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    Good eye, D H. I'll bet that's it.
     
  11. Jun 21, 2007 #10
    so the book is wrong then...
     
  12. Jun 21, 2007 #11

    Doc Al

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    One of you must be. For the problem as you described it here, your solution is correct. (Make sure you copied it correctly, as D H suggested.)
     
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