## anonymous one year ago question

1. anonymous

|dw:1433512332090:dw|

2. anonymous

@Loser66

3. Loser66

R can be understood as direction $$\mathbb R$$ is one direction |dw:1433512991259:dw|

4. Loser66

$$\mathbb R^2$$ is 2 dimensions

5. Loser66

|dw:1433513046896:dw|

6. Loser66

$$\mathbb R^3$$ is 3 dimensions |dw:1433513079018:dw|

7. anonymous

that's a really stupid notation when u could just say we're working in 3 dimensions!!!

8. Loser66

$$\vec r(t)=< f(t), g(t) >$$ is parametric vector

9. anonymous

what's the meaning of those less than greater than symbols?

10. Loser66

That is just the notation for YOU to realize that is a parametric vector form

11. anonymous

I know $\vec r(f(t),g(t))=f(t)i+g(t)j$

12. Loser66

For example: you have distance , velocity and time. You can graph a distance w.r.t time by the graph with x-axis represents|dw:1433513283150:dw| time and y-axis represents distance

13. Loser66

same as velocity and time |dw:1433513309349:dw|

14. Loser66

What if I want you to graph distanc/ velocity and both w.r.t time?

15. Loser66

Use parametric equations to jot them out.

16. anonymous

I simply know that $\vec r(x,y,z)=x i+yj+zk$ now be it x or x(t) either way we will have $\vec r(x(t),y(t),z(t))=x(t)i+y(t)j+z(t)k$ I just don't understand those curly braces

17. Loser66

Think of this, an accident happens. A car felt down a cliff. |dw:1433513446289:dw|

18. Loser66

if it is just an accident, the car's position should be as shown. But it is not, it is here |dw:1433513523649:dw|

19. Loser66

Parametric equations answer those question. If you understand why we have to know them, it inspires you a lllllllllllot

20. anonymous

tell me one thing, $\vec r=<3,4,5>$ is this the same as $3i+4j+5k$

21. Loser66

yup

22. Loser66

Have you ever take linear algebra??

23. anonymous

I've studied vectors but I've never seen this notation in my school

24. Loser66

Do you accept 1 dimension?

25. anonymous

what do u mean ?

26. Loser66

Do you understand number line? it is 1 dimension |dw:1433513798994:dw|

27. anonymous

of course I do

28. Loser66

Do you accept 2 dimensions? |dw:1433513841395:dw|

29. anonymous

yep...

30. Loser66

31. anonymous

yes, but how is that relevant?I simply wanted to know what those notations were for, I've never seen them before.

32. Loser66

1D---yes 2D----yes 3D----yes why not 4D, 5D.......nD??? Because you don't know them, you reject them? so that you said "that's a really stupid notation when u could just say we're working in 3 dimensions!!!"

33. anonymous

Is it also correct to say that if $\vec r(t)=<f(t),g(t),h(t)>$$\vec r(t)=f(t)i+g(t)j+h(t)k$

34. Loser66

yes

35. anonymous

Alright I understand this notation now

36. anonymous

thx

37. Loser66

the t in $$r(t),f(t), g(t)$$ shows all function are w.r.t t

38. anonymous

I'm not rejection higher dimensions but if you're working in 4 dimensions u can simply say in 4 dimensional space

39. Loser66

and the comma or i, j, k show they are linearly independent variable.

40. Loser66

But they are all relate to each other. In $$\mathbb R^3$$ when x =0, it can't become $$\mathbb R^2$$