# Homework Help: Vector Calculus

1. Dec 4, 2005

### Electro

Hello everyone,
I found a random question regarding finding the parametric equations for a tangent line to a space curve and I'm striving to solve it, but no results. I consulted the book but there isn't anything similar.

Find the parametric equations for the tangent line to the space curve:
x = ln(t), y = 2*Sqrt(t), z = t^2 at the point (0,2,1)

I would appreciate any suggesstions or hints how to solve it.
Thanks

2. Dec 4, 2005

### Tide

The time derivative of $\vec x$ is tangent to the curve. If $\vec v = d\vec x/dt$ then the line you are looking for is given by $\vec x_{tangent} = \vec x_0 + \vec v(t = t_0) (t - t_0)$ where $t_0$ is the time corresponding to the point of interest.