## ParthKohli Group Title Are standard basis vectors constant? one year ago one year ago

1. UnkleRhaukus Group Title

no, what do you mean

2. lgbasallote Group Title

are vectors even important?

3. lgbasallote Group Title

or better yet...is Math important?

4. ParthKohli Group Title

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 Group Title

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

6. ParthKohli Group Title

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

7. hartnn Group Title

i must be <1,0,0>

8. lgbasallote Group Title

yes you are

9. ParthKohli Group Title

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

10. lgbasallote Group Title

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

11. ParthKohli Group Title

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

12. lgbasallote Group Title

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

13. lgbasallote Group Title

no they are not

14. ParthKohli Group Title

OK

15. hartnn Group Title

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 Group Title

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

17. ParthKohli Group Title

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

18. ParthKohli Group Title

Yeah... @hartnn that's right!

19. lgbasallote Group Title

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

20. ParthKohli Group Title

Yeah, I do!

21. UnkleRhaukus Group Title

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

22. lgbasallote Group Title

+ 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 Group Title

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

24. hartnn Group Title

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

25. lgbasallote Group Title

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 Group Title

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 Group Title

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 Group Title

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

29. lgbasallote Group Title

yes. vectors are hard to grasp

30. UnkleRhaukus Group Title

in polar coordinates the basis vectors change direction

31. lgbasallote Group Title

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

32. ParthKohli Group Title

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 Group Title

none of us is 12 years old.

34. ParthKohli Group Title

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

35. UnkleRhaukus Group Title

the difference is 1 year

36. ParthKohli Group Title

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

37. lgbasallote Group Title

with age comes wisdom

38. ParthKohli Group Title

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

39. Ishaan94 Group Title

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

40. hartnn Group Title

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

41. lgbasallote Group Title

eww @Ishaan94 learn math

42. ParthKohli Group Title

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 Group Title

right

44. Ishaan94 Group Title

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

45. ParthKohli Group Title

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

46. Ishaan94 Group Title

No. I don't think so.

47. lgbasallote Group Title

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 Group Title

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

49. ParthKohli Group Title

That's what YOU believe.

50. hartnn Group Title

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

51. lgbasallote Group Title

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

52. ParthKohli Group Title

lol

53. lgbasallote Group Title

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

54. lgbasallote Group Title

that is also why you should not disturb the status quo

55. ParthKohli Group Title

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

56. lgbasallote Group Title

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

57. ParthKohli Group Title

For example?

58. hartnn Group Title

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

59. ParthKohli Group Title

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

60. ParthKohli Group Title

Thus, not leaving fundamentals.

61. Ishaan94 Group Title

How much time did you spend on Algebra, Trig?

62. lgbasallote Group Title

however, you skipped topics

63. ParthKohli Group Title

@Ishaan94 a lot

64. lgbasallote Group Title

there's a reason they give 4 years to algebra

65. Ishaan94 Group Title

I would need a definitive answer.

66. ParthKohli Group Title

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

67. lgbasallote Group Title

it's not because people are slow-learners

68. Ishaan94 Group Title

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 Group Title

agreed

70. ParthKohli Group Title

g2g :) thanks all!

71. lgbasallote Group Title

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 Group Title

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

73. Ishaan94 Group Title

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 Group Title

he still has other subjects though. math is not everything

75. Ishaan94 Group Title

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