1. Parametric equations, parallel line

This is a question from my calculus 3 class.

"Find the parametric equation of the line through the origin that is parallel to the line given by x = 1, y = -1 + t, z = 2."

I'm not sure if I did this right, and frankly I'm still a little uneasy with parametric equations.

So to begin, I made a vector out of the parametric equations they gave me just for the heck of it:
v = <1, 1, 0>

In the given equations:
x_0 = 0
y_0 = -1
z_0 = 2

And so the parallel line would have:
x_0 = 0
y_0 = 0
z_0 = 0

Making the parallel parametric equations through the origin:
x = t
y = t
z = t

I don't feel this is correct, but my logic behind the answer is that if the line goes through the origin, then only the above parametric equations work right? Honestly I'm confused. I guess I need a bump in the right direction.

2. Or wait.. would the equations be:
x = t
y = t
z = 0

3. $\displaystyle \begin{Bmatrix}x=0\\y=t\\z=0\end{matrix} \quad (t\in\mathbb{R})$

Fernando Revilla

4. I'm a little confused on how to get that answer.

I'm going by the equations:
x = x_0 + a*t
y = y_0 + b*t
z = z_0 + c*t

And so:
a = 1
b = 1
c = 0

The x_0, y_0, and z_0 are all zero.

And I get this:
x = t
y = t
z = 0

5. Originally Posted by nautica17
And so:
a = 1
b = 1
c = 0

According to the OP it should be:

$\displaystyle a=0,\;b=1,\;c=0$

Fernando Revilla