# Thread: Parametric Representation of a Curve

1. ## Parametric Representation of a Curve

I'm sure this is easy but my math is a bit rusty.

I need to find the parametric representation of the following curve:

a straight line through (5,1,2) and (11,3,0)

THANKS!!

2. So a parametric representation breaks this down into 3 components, x(t),y(t) and z(t). Call the point (5,1,2) the initial point of the curve and (11,3,0) the terminal point. We're writing these with respect to time, t, so just to make things easy let t go from 0 to 1.

At t=0, we are at the initial point, so....

x(t)=5
y(t)=1
z(t)=2

Now we have to add a term to each such that each component ends at it's corresponding terminal point.

x(t)=5+6t
y(t)=1+2t
z(t)=2-2t , where t runs from 0 to 1.

Make sense?