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ParthKohli

  • 2 years ago

Are standard basis vectors constant?

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  1. UnkleRhaukus
    • 2 years ago
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    no, what do you mean

  2. lgbasallote
    • 2 years ago
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    are vectors even important?

  3. lgbasallote
    • 2 years ago
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    or better yet...is Math important?

  4. ParthKohli
    • 2 years ago
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    In one of the examples, I noticed that they made a quick substitution for the following vectors:\[\overrightarrow{i} = \langle 0,0,1\rangle\]\[\overrightarrow{j} = \langle 0,1,0\rangle\]\[\overrightarrow k = \langle0,0,1\rangle\]So are vector i, vector j and vector k defined vectors?

  5. lgbasallote
    • 2 years ago
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    im thinking these are \(\hat i, \; \hat j, \; \hat k\) for some reason

  6. ParthKohli
    • 2 years ago
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    http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx "Standard Basis Vectors Revisited"

  7. hartnn
    • 2 years ago
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    i must be <1,0,0>

  8. lgbasallote
    • 2 years ago
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    yes you are

  9. ParthKohli
    • 2 years ago
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    Oh yes,\[\overrightarrow{i} = \langle1,0,0\rangle\]Sorry... messed up

  10. lgbasallote
    • 2 years ago
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    still thinking that's supposed to be \(\hat i\)

  11. ParthKohli
    • 2 years ago
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    OK, but is \(\hat{i}\) the same as \(\overrightarrow{i}\)?

  12. lgbasallote
    • 2 years ago
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    \[\hat i = \; \text{positive x-axis}\]

  13. lgbasallote
    • 2 years ago
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    no they are not

  14. ParthKohli
    • 2 years ago
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    OK

  15. hartnn
    • 2 years ago
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    and yes, i is defined as unit vector in x direction j is defined as unit vector in y direction k is defined as unit vector in z direction and denoted by i^ as said by lg

  16. lgbasallote
    • 2 years ago
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    \[\vec i \implies \text{vector}\] \[\hat i \implies \text{vector component}\]

  17. ParthKohli
    • 2 years ago
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    I don't really get any of those, but thanks :P

  18. ParthKohli
    • 2 years ago
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    Yeah... @hartnn that's right!

  19. lgbasallote
    • 2 years ago
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    think of it somehow like this: i => x j => y k => z

  20. ParthKohli
    • 2 years ago
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    Yeah, I do!

  21. UnkleRhaukus
    • 2 years ago
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    \[\vec\imath=\langle 1,0,0\rangle\]\[\vec\jmath=\langle 0,1,0\rangle\]\[\vec k=\langle 0,0,1\rangle\]

  22. lgbasallote
    • 2 years ago
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    + i => positive x-axis -i => negative x-axis + j => positive y-axis - j => negative y-axos k => positive z axis -k => negative z-axis

  23. ParthKohli
    • 2 years ago
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    That's a nice way to handle it! :)

  24. hartnn
    • 2 years ago
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    can u imagine a vector along x-direction and magnitude = 1.......thats i|dw:1347180055694:dw|

  25. lgbasallote
    • 2 years ago
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    one more thing you should know, the expression for vectors is given as \[\vec A = x\hat i + y\hat j + z\hat k\] or something like that

  26. lgbasallote
    • 2 years ago
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    that means i is a vector component for x j is a vector component for y k is a vector component for z

  27. lgbasallote
    • 2 years ago
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    so when you have \[\hat i\] that means \[\vec A = 1\hat i + 0\hat j + 0\hat k\] so there's no value for y or z so it just lies on +x-axiis

  28. ParthKohli
    • 2 years ago
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    lol, thanks... I don't think I can really get it now. I'm not a genius :P

  29. lgbasallote
    • 2 years ago
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    yes. vectors are hard to grasp

  30. UnkleRhaukus
    • 2 years ago
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    in polar coordinates the basis vectors change direction

  31. lgbasallote
    • 2 years ago
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    btw... why are you so keen in learning new things all the time @ParthKohli ?

  32. ParthKohli
    • 2 years ago
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    Because I can't stand the fact that I can't answer so many questions on the site, and there are people like you who know a lot. :|

  33. lgbasallote
    • 2 years ago
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    none of us is 12 years old.

  34. ParthKohli
    • 2 years ago
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    I'm 13 lol, and I don't think that age makes a difference :)

  35. UnkleRhaukus
    • 2 years ago
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    the difference is 1 year

  36. ParthKohli
    • 2 years ago
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    I mean that age contributes nothing to how much a person knows...

  37. lgbasallote
    • 2 years ago
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    with age comes wisdom

  38. ParthKohli
    • 2 years ago
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    Actually, I should be ashamed that it took me 13 long years do this all.

  39. Ishaan94
    • 2 years ago
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    I think your time is better spent on learning mathematics than thinking about all this :-)

  40. hartnn
    • 2 years ago
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    lol,so u wanted to know everything from birth!!??

  41. lgbasallote
    • 2 years ago
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    eww @Ishaan94 learn math

  42. ParthKohli
    • 2 years ago
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    We evolved with certain rules that made no sense. For example: 1) Babies are supposed to play with toys. 2) Adults are supposed to watch movies with stripping scenes. 3) Kids don't know anything. I feel that it is *us* who evolved with these beliefs :) a baby can do calculus as well, but we made the baby play with toys.

  43. lgbasallote
    • 2 years ago
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    right

  44. Ishaan94
    • 2 years ago
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    An average baby doesn't have the necessary IQ to do calculus.

  45. ParthKohli
    • 2 years ago
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    WE MADE HIS IQ DOWN BY MAKING HIM PLAY WITH TOYS.

  46. Ishaan94
    • 2 years ago
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    No. I don't think so.

  47. lgbasallote
    • 2 years ago
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    to learn calculus you need to know algebra. to know algebra you need to know arithmetic. to know arithmetic you need to know kinesthetics

  48. Ishaan94
    • 2 years ago
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    In fact a playful childhood might help better in developing one's mind.

  49. ParthKohli
    • 2 years ago
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    That's what YOU believe.

  50. hartnn
    • 2 years ago
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    a baby is supposed to enjoy, not learn math ..... thats why we me him/her to play ....

  51. lgbasallote
    • 2 years ago
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    if your theory is right @ParthKohli then i can confidently concur that online schools educates people very well

  52. ParthKohli
    • 2 years ago
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    lol

  53. lgbasallote
    • 2 years ago
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    online schools miseducate people because they keep jumping from topics to topics; skipping fundamentals

  54. lgbasallote
    • 2 years ago
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    that is also why you should not disturb the status quo

  55. ParthKohli
    • 2 years ago
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    I'm... not.... jumping, right?

  56. lgbasallote
    • 2 years ago
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    you are. you're trying to learn this without the necessary fundamentals

  57. ParthKohli
    • 2 years ago
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    For example?

  58. hartnn
    • 2 years ago
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    i think u are going fast just because u want to answer more questions here..

  59. ParthKohli
    • 2 years ago
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    Yeah, I am, but I didn't skip algebra... and I didn't skip logarithms... not even trigonometry.

  60. ParthKohli
    • 2 years ago
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    Thus, not leaving fundamentals.

  61. Ishaan94
    • 2 years ago
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    How much time did you spend on Algebra, Trig?

  62. lgbasallote
    • 2 years ago
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    however, you skipped topics

  63. ParthKohli
    • 2 years ago
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    @Ishaan94 a lot

  64. lgbasallote
    • 2 years ago
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    there's a reason they give 4 years to algebra

  65. Ishaan94
    • 2 years ago
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    I would need a definitive answer.

  66. ParthKohli
    • 2 years ago
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    But I have managed to do it early... nothing's really wrong!

  67. lgbasallote
    • 2 years ago
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    it's not because people are slow-learners

  68. Ishaan94
    • 2 years ago
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    Parth I think you should spend your time more on Algebra and Trig. Calculus isn't tricky. IMO doesn't even asks question from calculus. Get a good book on Algebra and start solving it.

  69. lgbasallote
    • 2 years ago
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    agreed

  70. ParthKohli
    • 2 years ago
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    g2g :) thanks all!

  71. lgbasallote
    • 2 years ago
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    honestly @Ishaan94 don't you think kohli could be a valedictorian if only he tried using the time he spends doing calculus to just master algebra? if he has this kind of knowledge on calc, then he must hve spent a lot of time, enough to have made him a valedictorian

  72. lgbasallote
    • 2 years ago
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    i think it's a false cause to study for OpenStudy rather than to study for academics

  73. Ishaan94
    • 2 years ago
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    hmm I am not against Parth learning Calculus but the thing is Algebra could be a lot trickier than Calculus. So it's really important that one spends significant amount of time on Algebra. As for academics I don't think 8th grade is really complex. He could still be a valedictorian. :-)

  74. lgbasallote
    • 2 years ago
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    he still has other subjects though. math is not everything

  75. Ishaan94
    • 2 years ago
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    I might be wrong person to discuss about getting grades in school. I never really payed much attention to grades.

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