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R can be understood as direction \(\mathbb R\) is one direction |dw:1433512991259:dw|
\(\mathbb R^2\) is 2 dimensions
\(\mathbb R^3\) 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 \[3i+4j+5k\]
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|
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)=
Alright I understand this notation now
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 \(\mathbb R^2\)