1. Position Vectors

What exactly are position vectors? I happened to be out on the day this was taught and I have a quarterly coming up, help?
show me an example with this problem: find the position vector:
v(t)= <-sin t, cos t> and r(0)= <0,1>

What exactly are position vectors? I happened to be out on the day this was taught and I have a quarterly coming up, help?
show me an example with this problem: find the position vector:
v(t)= <-sin t, cos t> and r(0)= <0,1>
$v(t) = \left<-sin{t} ,\cos{t} \right>
$

antiderivative of each component ...

$r(t) = \left<\cos{t}+C ,\sin{t}+C \right>$

use the given initial condition to find $C$ for each component.

a position vector gives the x and y components of position at any time t.