# Homework Help: Parameterized tangent line to a parameterized curve

1. Feb 10, 2009

### Cauchy1789

1. The problem statement, all variables and given/known data

I seem to remember that a parameterized a(t) curve in $$\mathbb{R}^3$$ that one can construct the tangent from the slope of a'(t) and the curve itself.

such that the tangent line L = a(t) + s * a'(t) to a. This is supposedly a straight line in $$\mathbb{R}^3$$.
To make a long question. What theorem allows me to construct the tangent in such a way? confused:

2. Feb 10, 2009

### tiny-tim

Hi Cauchy1789!

It's the theorem that says that the slope of the tangent euqals the derivative …

so, for fixed t, L(s) = s * a'(t) + constant …

and the constant has to be a(t) because L(0) = a(t).