## ParthKohli Group Title Are standard basis vectors constant? 2 years ago 2 years ago

1. UnkleRhaukus

no, what do you mean

2. lgbasallote

are vectors even important?

3. lgbasallote

or better yet...is Math important?

4. ParthKohli

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

im thinking these are $$\hat i, \; \hat j, \; \hat k$$ for some reason

6. ParthKohli

http://tutorial.math.lamar.edu/Classes/CalcII/VectorArithmetic.aspx "Standard Basis Vectors Revisited"

7. hartnn

i must be <1,0,0>

8. lgbasallote

yes you are

9. ParthKohli

Oh yes,$\overrightarrow{i} = \langle1,0,0\rangle$Sorry... messed up

10. lgbasallote

still thinking that's supposed to be $$\hat i$$

11. ParthKohli

OK, but is $$\hat{i}$$ the same as $$\overrightarrow{i}$$?

12. lgbasallote

$\hat i = \; \text{positive x-axis}$

13. lgbasallote

no they are not

14. ParthKohli

OK

15. hartnn

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

$\vec i \implies \text{vector}$ $\hat i \implies \text{vector component}$

17. ParthKohli

I don't really get any of those, but thanks :P

18. ParthKohli

Yeah... @hartnn that's right!

19. lgbasallote

think of it somehow like this: i => x j => y k => z

20. ParthKohli

Yeah, I do!

21. UnkleRhaukus

$\vec\imath=\langle 1,0,0\rangle$$\vec\jmath=\langle 0,1,0\rangle$$\vec k=\langle 0,0,1\rangle$

22. lgbasallote

+ 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

That's a nice way to handle it! :)

24. hartnn

can u imagine a vector along x-direction and magnitude = 1.......thats i|dw:1347180055694:dw|

25. lgbasallote

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

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

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

lol, thanks... I don't think I can really get it now. I'm not a genius :P

29. lgbasallote

yes. vectors are hard to grasp

30. UnkleRhaukus

in polar coordinates the basis vectors change direction

31. lgbasallote

btw... why are you so keen in learning new things all the time @ParthKohli ?

32. ParthKohli

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

none of us is 12 years old.

34. ParthKohli

I'm 13 lol, and I don't think that age makes a difference :)

35. UnkleRhaukus

the difference is 1 year

36. ParthKohli

I mean that age contributes nothing to how much a person knows...

37. lgbasallote

with age comes wisdom

38. ParthKohli

Actually, I should be ashamed that it took me 13 long years do this all.

39. Ishaan94

I think your time is better spent on learning mathematics than thinking about all this :-)

40. hartnn

lol,so u wanted to know everything from birth!!??

41. lgbasallote

eww @Ishaan94 learn math

42. ParthKohli

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

right

44. Ishaan94

An average baby doesn't have the necessary IQ to do calculus.

45. ParthKohli

WE MADE HIS IQ DOWN BY MAKING HIM PLAY WITH TOYS.

46. Ishaan94

No. I don't think so.

47. lgbasallote

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

In fact a playful childhood might help better in developing one's mind.

49. ParthKohli

That's what YOU believe.

50. hartnn

a baby is supposed to enjoy, not learn math ..... thats why we me him/her to play ....

51. lgbasallote

if your theory is right @ParthKohli then i can confidently concur that online schools educates people very well

52. ParthKohli

lol

53. lgbasallote

online schools miseducate people because they keep jumping from topics to topics; skipping fundamentals

54. lgbasallote

that is also why you should not disturb the status quo

55. ParthKohli

I'm... not.... jumping, right?

56. lgbasallote

you are. you're trying to learn this without the necessary fundamentals

57. ParthKohli

For example?

58. hartnn

i think u are going fast just because u want to answer more questions here..

59. ParthKohli

Yeah, I am, but I didn't skip algebra... and I didn't skip logarithms... not even trigonometry.

60. ParthKohli

Thus, not leaving fundamentals.

61. Ishaan94

How much time did you spend on Algebra, Trig?

62. lgbasallote

however, you skipped topics

63. ParthKohli

@Ishaan94 a lot

64. lgbasallote

there's a reason they give 4 years to algebra

65. Ishaan94

I would need a definitive answer.

66. ParthKohli

But I have managed to do it early... nothing's really wrong!

67. lgbasallote

it's not because people are slow-learners

68. Ishaan94

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

agreed

70. ParthKohli

g2g :) thanks all!

71. lgbasallote

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

i think it's a false cause to study for OpenStudy rather than to study for academics

73. Ishaan94

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

he still has other subjects though. math is not everything

75. Ishaan94

I might be wrong person to discuss about getting grades in school. I never really payed much attention to grades.