Activity 13.3.2

For each curve below, find a parametrization of the curve. Ensure that each curve's orientation matches the one specified.

1. The line segment in $\R^3$ from $(0,1,-2)$ to $(3,-1,2)$.

2. The line segment in $\R^3$ from $(3,-1,2)$ to $(0,1,-2)$.

3. The circle of radius $3$ (in $\R^2$) centered at the origin, beginning at the point $(0,-3)$ and proceeding clockwise around the circle.

4. In $\R^2$, the portion of the parabola $y^2 = x$ from the point $(4,2)$ to the point $(1,-1)$.