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Cross product and dot product scalars

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)?


    2. Relevant equations
    Know how to do the cross product and dot product

    3. The attempt at a solution
    For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an online program that only has one box to type in?
     
  2. jcsd
  3. Feb 12, 2008 #2

    Kurdt

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    Your answer should be a scalar anyway if you had to take the dot product (commonly known as the scalar product). I suggest you check your answer.
     
  4. Feb 12, 2008 #3
    I didnt think my answer was wrong though?
     
  5. Feb 12, 2008 #4

    Kurdt

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    If you take the dot product of two vectors then the answer will be a scalar not a vector. If you post what you've done it'll be easier to identify where you went wrong.
     
  6. Feb 12, 2008 #5
    First i calculated the quantity of d1+d2 and got 13i + 0j +8k. Then i went to the other side of the problem and distributed the 4 to the d2 terms and got a result of 36i - 40j + 24k. After that, i took the cross product of d1 and 4d2 and got -160i -24j - 200k. Then i took the dot product and got -2080i - 1600k (sorry i posted the wrong answer the first time, my bad)
     
  7. Feb 12, 2008 #6

    Kurdt

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    For the addition of d1 and d2, -10 +(-10) does not equal 0.

    For the cross product, that should be +200k.

    The dot product of two vectors is:

    [tex] \mathbf{a}\cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z [/tex]
     
    Last edited: Feb 12, 2008
  8. Feb 12, 2008 #7
    so then when i add that up, it equals one number? for example if i had axbx=3, ayby=4 and azbz=2, then i would have something that resembles 3+4+2 and would i use 9 for the answer?
     
  9. Feb 12, 2008 #8
    yes, thats correct.
     
  10. Feb 12, 2008 #9
    i got -3200 for my final answer, but that seems wrong..
     
  11. Feb 12, 2008 #10

    Kurdt

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    Again if you post exactly what you've done when computing the dot product it will be easier to advise you where you went wrong.
     
  12. Feb 12, 2008 #11
    after doing the cross product for d1xd2, i got -160i -24j -200k. After that, i multiplied by the sum i got for the d1+d2 section. So in the end, i multiplied -160 times 13, -24 times -20, and -200 times 8. Then i had -2080 + 480 - 1600
     
  13. Feb 12, 2008 #12

    Kurdt

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    If you look in my previous post I said that after the cross product you should have +200k not -200k.
     
  14. Feb 12, 2008 #13
    remeber that the cross product is something like;

    [-,-]: VxV----->V; \\ V=vector space

    so gives you back another vector;

    while the dot product (generally an inner product) is something like;

    (-,-): VxV------>C \\ C=complex field

    know how to make both in an euclidean orthonormal basis and you'll get your answer;

    regards;
    marco;
     
  15. Feb 12, 2008 #14
    got it, thanks guys...sorry for bein dumb (sick last few days)
     
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