im having trouble figuring out what the problem wants me to find.
Find a path that traces the circle in the plane with radius and center with constant speed 8.
thanks in advance!
The best way to do this is to parameterize x, y and z. Since we're working in the plane y=-1, y is easy enough to parametrize, it's just y=-1. x and z are a little more difficult. Let's imagine for right now that the circle were centred at the origine, then x and z can be expressed as
$\displaystyle
x=r\, cos(wt)
$
$\displaystyle
z=r\, sin(wt)
$
where r is the radius of the circle (r=2), t is the time and w is a constant we'll have to find for ourselves (it relates to the speed). Note also that the choice of cos for x and sin for z is arbitrary, we could have gone sin for x and cos for z.
Now since the center has to be (3, -1, 2), just add 3 to x and 2 to z:
$\displaystyle
x=2\, cos(wt)+3
$
$\displaystyle
z=2\, sin(wt)+2
$
From here all you have to do is find w and you're all done. Let me know if you need any more help on this.