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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1433512332090:dw|
R can be understood as direction \(\mathbb R\) is one direction |dw:1433512991259:dw|

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\(\mathbb R^2\) is 2 dimensions
|dw:1433513046896:dw|
\(\mathbb R^3\) is 3 dimensions |dw:1433513079018:dw|
that's a really stupid notation when u could just say we're working in 3 dimensions!!!
\(\vec r(t)=< f(t), g(t) >\) is parametric vector
what's the meaning of those less than greater than symbols?
That is just the notation for YOU to realize that is a parametric vector form
I know \[\vec r(f(t),g(t))=f(t)i+g(t)j\]
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
same as velocity and time |dw:1433513309349:dw|
What if I want you to graph distanc/ velocity and both w.r.t time?
Use parametric equations to jot them out.
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
Think of this, an accident happens. A car felt down a cliff. |dw:1433513446289:dw|
if it is just an accident, the car's position should be as shown. But it is not, it is here |dw:1433513523649:dw|
Parametric equations answer those question. If you understand why we have to know them, it inspires you a lllllllllllot
tell me one thing, \[\vec r=<3,4,5>\] is this the same as \[3i+4j+5k\]
yup
Have you ever take linear algebra??
I've studied vectors but I've never seen this notation in my school
Do you accept 1 dimension?
what do u mean ?
Do you understand number line? it is 1 dimension |dw:1433513798994:dw|
of course I do
Do you accept 2 dimensions? |dw:1433513841395:dw|
yep...
How about 3 dimensions?
yes, but how is that relevant?I simply wanted to know what those notations were for, I've never seen them before.
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!!!"
Is it also correct to say that if \[\vec r(t)=\]\[\vec r(t)=f(t)i+g(t)j+h(t)k\]
yes
Alright I understand this notation now
thx
the t in \(r(t),f(t), g(t)\) shows all function are w.r.t t
I'm not rejection higher dimensions but if you're working in 4 dimensions u can simply say in 4 dimensional space
and the comma or i, j, k show they are linearly independent variable.
But they are all relate to each other. In \(\mathbb R^3\) when x =0, it can't become \(\mathbb R^2\)

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