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|dw:1433512332090:dw|

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

\(\mathbb R^2\) 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 \[\vec r(f(t),g(t))=f(t)i+g(t)j\]

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.

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

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?

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

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 \(\mathbb R^2\)