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anonymous

  • one year ago

PLEASE HELP ME!!!!!!!!!!!!! I have no idea where to start? Evaluate the expression: v ⋅ w Given the vectors: r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2>

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  1. nuttyliaczar
    • one year ago
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    Dot products are scalar products that you obtain by multiplying each of the like dimensions with each other and then adding all of the products

  2. anonymous
    • one year ago
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    Do i use the formula u x v= (u2v3 - u3v2)i - (u1v3 - u3v1)j + (u1v2 - u2v1)k ?

  3. anonymous
    • one year ago
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    Oh, you mean multiplying them all together? @nuttyliaczar

  4. nuttyliaczar
    • one year ago
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    We're just looking at vectors v and w here so ignore the first. There will be three products here since both vectors have three dimensions/components. The first product is (6)(-7)=-42

  5. anonymous
    • one year ago
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    Okay, so the second and third product would be 7(5)=35 and -3(2)=-6

  6. anonymous
    • one year ago
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    Then will our simplified expression look like <-42, 35, -6> * <8, 1, -6>? @nuttyliaczar

  7. nuttyliaczar
    • one year ago
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    Oh no no you want to add the products after

  8. nuttyliaczar
    • one year ago
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    Dot products are scalar values, meaning they only have a magnitude, no direction

  9. anonymous
    • one year ago
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    Oh, so does that mean we add -42+35+(-6)? @nuttyliaczar

  10. nuttyliaczar
    • one year ago
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    Yes, that will get you your dot product between v and w

  11. anonymous
    • one year ago
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    Okay so that would be -13, right? Then what do we do with r = <8, 1, -6>?

  12. anonymous
    • one year ago
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    @nuttyliaczar

  13. nuttyliaczar
    • one year ago
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    The r is irrelevant to the question, so we can ignore it. And yes it is -13

  14. anonymous
    • one year ago
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    Oh! Right, I just took another look at the question. So my final answer would be just -13 @nuttyliaczar

  15. nuttyliaczar
    • one year ago
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    And while we are on this topic, what does this dot product tell you about the vectors? For example, what would happen if you had two perpendicular vectors?

  16. nuttyliaczar
    • one year ago
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    Yes just -13

  17. anonymous
    • one year ago
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    Im not sure about your question @nuttyliaczar I think the angle between the vectors would be 90 degrees..

  18. nuttyliaczar
    • one year ago
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    I mean what would the dot product of two perpendicular vectors be?

  19. anonymous
    • one year ago
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    Would it be zero? @nuttyliaczar

  20. anonymous
    • one year ago
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    Im sorry, I have not really gone over this much @nuttyliaczar

  21. nuttyliaczar
    • one year ago
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    Yes, because the products when added would cancel each other out

  22. nuttyliaczar
    • one year ago
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    It's okay, just giving you some insight on what dot products are useful for

  23. anonymous
    • one year ago
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    Thank you so much for helping me and providing me some insight, I really appreciate it! @nuttyliaczar

  24. nuttyliaczar
    • one year ago
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    No problem, good luck in your future endeavours

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