1. Another Calc III Problem

Here's the problem:
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point:

$x = e^-t * cos(t)$
$y = e^-t * sin(t)$
$z = e^-t$
At the point: (1,0,1)

(It's supposed to be e to the negative t, I just can't get the math software to work properly).

I know the answer is supposed to be:
$x = 1-t$
$y = t$
$z = 1-t$

but I have no idea how to get there! Help!

2. Originally Posted by saxyliz
Here's the problem:
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point:

$x = e^-t * cos(t)$
$y = e^-t * sin(t)$
$z = e^-t$
At the point: (1,0,1)

(It's supposed to be e to the negative t, I just can't get the math software to work properly).

I know the answer is supposed to be:
$x = 1-t$
$y = t$
$z = 1-t$

but I have no idea how to get there! Help!
let our curve be given by $r(t) = \left< x(t), y(t), z(t) \right> = \left$.

note that the line we want is the line passing through the point (1,0,1) with direction vector given by $r'(t)$.

now we are concerned with when $t = 0$ (since in that case, x = 1, y = 0 and z = 1, hence we are passing through the point (1,0,1))

So, you want the line passing through (1,0,1) that has direction vector $r'(0)$

i trust you can take it from here

3. Thanks! I understand it now!