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Hoa

show that if vector v is orthogonal with vector w and u, then v orthogonal with (kw + mu) for all k and m. Please help

  • one year ago
  • one year ago

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  1. TuringTest
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    If two vectors are orthogonal, then their dot product is zero\[\vec v\perp\vec w\implies\vec v\cdot\vec w=0\]now remember that constants can be factored our of the dot product\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)\]and that the dot product is distributive\[\vec v\cdot(\vec u+\vec w)=\vec v\cdot\vec w+\vec v\cdot\vec u\]

    • one year ago
  2. Hoa
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    yes. then? I got something not what i want. please, give me more

    • one year ago
  3. TuringTest
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    I'm not going to do the whole problem, I am just here to guide you. Take the dot product following what I have written above to evaluate\[\vec v\cdot(k\vec w+m\vec u)\]What do you get?

    • one year ago
  4. Hoa
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    v.mu +v.kw

    • one year ago
  5. TuringTest
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    right, now how do the constants affect the dot product?

    • one year ago
  6. Hoa
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    m+k

    • one year ago
  7. TuringTest
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    no, the scalars can be factored out of dot product multiplication\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)=?\]

    • one year ago
  8. Hoa
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    kv.w

    • one year ago
  9. TuringTest
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    and what is \(\vec v\cdot\vec w\) ?

    • one year ago
  10. Hoa
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    0

    • one year ago
  11. TuringTest
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    yes, so then what is\[\vec v\cdot(k\vec w)\]?

    • one year ago
  12. Hoa
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    0

    • one year ago
  13. TuringTest
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    yes, so then what is\[\vec v\cdot(k\vec w+m\vec u)\]?

    • one year ago
  14. Hoa
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    i got it now. my bad when make them = instead of adding together to get the answer, thanks a lot

    • one year ago
  15. TuringTest
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    you're welcome!

    • one year ago
  16. Hoa
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    Let me put everything in neat, would you please check it for me?

    • one year ago
  17. Hoa
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    how to put orthogonal symbol?

    • one year ago
  18. TuringTest
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    \perp

    • one year ago
  19. Hoa
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    don't understand

    • one year ago
  20. ParthKohli
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    \(\backslash ( \text{\perp}\backslash ) \)

    • one year ago
  21. TuringTest
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    are you trying to use the equation editor or are you writing in LaTeX ? ...yeah best is do what @ParthKohli wrote

    • one year ago
  22. ParthKohli
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    ``` \( v \perp u\) ```

    • one year ago
  23. Hoa
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    \(\perp\) Lol. got it. thanks

    • one year ago
  24. Hoa
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    i need time to practice how to use the symbol. do many time but delete all at the end, sorry , waste your time, I try and send you mine in perfect . thanks thanks a lot for help in material

    • one year ago
  25. Hoa
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    by the way how to put vector symbol

    • one year ago
  26. TuringTest
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    \[\backslash(\text{\vec u}\backslash)\], and if you want to get good at writing equations try learning the language LaTeX

    • one year ago
  27. Hoa
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    \(v\perp u\) ---> \(v\perp ku\) is it right?

    • one year ago
  28. Hoa
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    what LateX means

    • one year ago
  29. Hoa
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    \(v perp w\) ---> \(v perp mw\)

    • one year ago
  30. TuringTest
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    LaTeX is the language used to write the math symbols. enclose things in brackets like so: \[ code \.] or \( code \.) (do not put the period, I just did that to illustrate how to put the backslashes and brackets http://omega.albany.edu:8008/Symbols.html yes

    • one year ago
  31. Hoa
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    I will. thanks for all.

    • one year ago
  32. TuringTest
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    for what you are doing you should write\[\backslash [\text{\vec v \perp \vec w}\backslash ]\]backslashes and spaces are important

    • one year ago
  33. Hoa
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    \[\vec v\perp\vec w\]. bingo

    • one year ago
  34. TuringTest
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    nice :) keep practicing LaTeX, it's handy!

    • one year ago
  35. Hoa
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    I will. thank you very much.

    • one year ago
  36. Hoa
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    \[\vec v\perp\vec w\]---> \[\vec v\perp\k vec w\]

    • one year ago
  37. Hoa
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    ah .... mistake

    • one year ago
  38. TuringTest
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    You are welcome! another tip: if you want to know how somebody wrote something, hover your cursor over the latex you want to know the code for and press right click -> show math as -> Tex commands and you can see the source code and copy and paste it into\[\backslash[\dots\backslash]\text{ or }\backslash(\dots\backslash)\] It takes some practice to avoid syntax errors. The arrow can be done with \implies, though i? I think a double arrow is better here \iff (if and only if)

    • one year ago
  39. Hoa
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    k\(\vec v\). bingo

    • one year ago
  40. TuringTest
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    very good :D\[\backslash[\text{\vec v\perp \vec w\iff \vec v\cdot\vec w=0}\backslash]\]gives\[\vec v\perp \vec w\iff \vec v\cdot\vec w=0\]

    • one year ago
  41. ParthKohli
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    I never answered this question. A medal is definitely not needed here. Just doing my amby thing :-)

    • one year ago
  42. Hoa
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    i am using other's computer, and i don't know how to copy the conversation to read later or follow when practice. so i have to copy by hand what you guide. it takes time.

    • one year ago
  43. TuringTest
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    @parth But I never thought to show latex by writing \backslash the way you did, and that proved very useful :) @hoa typing in latex does take some time, but of course it becomes less when you get used to it.

    • one year ago
  44. ParthKohli
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    @hoa It took me a lot of time too!

    • one year ago
  45. Hoa
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    @ParthKohli . I don't know what you mean, but to me, being helpful person deserves all. I appreciate what others guide me.

    • one year ago
  46. Hoa
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    @ParthKohli . the net automatically put the medal , i didn't do. or other put it there

    • one year ago
  47. ParthKohli
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    Turing did. :-)

    • one year ago
  48. Hoa
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    yes. my question is: what does the medal mean?

    • one year ago
  49. TuringTest
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    Giving medals for best answer raises the recipients SmartScore. Parth and I have already gotten our fair share, that's why we're level 99.

    • one year ago
  50. Hoa
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    why ? to me, it's just for showing the appreciateness

    • one year ago
  51. ParthKohli
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    Mine wasn't too fair. :-P

    • one year ago
  52. TuringTest
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    I don't think most high-level users care much about scores and medals. It's just a sort of acknowledgement, but the teaching is what really matters.

    • one year ago
  53. Hoa
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    ok. I got it. I make question "iff" need explanation, so whenever there is someone helps me, i give medal to show my appreciation no matter what it 's the best answer or not . now, i know what it means, thanks

    • one year ago
  54. TuringTest
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    No, you should really only give a medal if you think the user really *deserves* it. Feel free not to give one for those who only try to give answers without teaching, of which there are many.

    • one year ago
  55. Hoa
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    they know who they are no matter how many medals they have, right? we are self- respect, they are the same. However, if you say so, I will be careful in giving medal. And if you say so, I feel my medal does not deserve at all. All my answer is for very very easy problems. shame on me

    • one year ago
  56. TuringTest
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    Don't feel bad, just help people in a way you can be proud of. Try to teach others, regardless of the level of the question and you will do great here!

    • one year ago
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