How do I get the parametrization?

[DrunkApple]

Homework Statement

Compute the line integral of the scalar function.
f(x,y,z) = x$e^{z^2}$, piecewise linear path from (0,0,1) to (0,2,0) to (1,1,1)

Homework Equations

The Attempt at a Solution

In this problem, all I need is a parametrization. First I drew the line from (0,0,1) to (0,2,0) xyz-plane. I got the slope as z = 1 - $\frac{y}{2}$. So I set y = t then z will be 1 - $\frac{t}{2}$. I got parametrization as c(t) = <0,t,1-$\frac{y}{2}$>. But it's wrong. It's c(t) = <0,2t,1-2t>. Would anyone help me how to get parametrization ??

 

[HallsofIvy]

Yes, the line from (0, 0, 1) to (0, 2, 0) can be written as z= 1- y/2. Since you are using t as parameter, that would be <0, t, 1- t/2>. Why do you say that is wrong?
When t= 0, your parameterization gives (0, 0, 1) and when t= 2, it gives (0, 2, 1). A line is determined by two points so it gives the correct line.

It is c(t)= <0, 2t, 1- 2t> that is wrong. In order that y= 2t= 2, t must be 1. But then z= 1- 2= -1, not 0.