- #1

Destroxia

- 204

- 7

## Homework Statement

Find parametric equations for the line through P1 and P2 and also for the line segment joining those points. Also find the conditions for the parametric equations.

a) P1(0, 2) and P2(-4,-4)

b) P1(7,-3,9) and P2(7, -3, 1)

## Homework Equations

Equation of a line (Vector Form): ## \vec r = \vec r_0 + t\vec v ##[/B]

## The Attempt at a Solution

[/B]

I've already solved the problem, my issue just lies in finding the conditions for the parametric equations as well.

a) x = -4t, y = 2 - 6t

b) x = 7, y = -3, z = 9 - 8t

Wouldn't the parametric equation work from ## -\infty ≤ t ≤ \infty ##

I see no reason why some parallel direction vector wouldn't be able to be multiplied by some scalar to equal the line vector. Any multiple, negative or positive should be able to give me any line that passes through those points.

So am I correct in my assumption that the conditions should be from ## -\infty ≤ t ≤ \infty ##