parametric equation and tangent line

• March 11th 2008, 11:15 PM
lllll
parametric equation and tangent line
I need some help finding a parametric equation for the tangent line to the curve:

$x= e^t, \ \ y=te^t, \ \ z= te^{t^2}, \ \ (1,0,0)$

Solution:
$x' = e^t, \ \ y'= e^t +te^t, \ \ z'=e^{t^2} + 2t^{2}e^{t^2}$

taking $r_0 + t(r_1)$ gives me $x=1+(e)t, \ \ y= (2e)t, \ \ z=(3e)t$

is this correct?