Finding Non-Negative Points on Line L: Vector Equations Explained

[skyturnred]

Homework Statement

So we are given the equation of a line and asked to do a bunch of stuff with it. When I get to the following question, I just don't understand what it is asking.

The line:

L=(2,2,5)+t(2,-1,1), where t is an element of the reals

Question:

Let S be the the line segment consisting of the points on L whose coordinates are all nonnegative (that is, S is the intersection of L with the first octant). Find the vector equation of S.

Homework Equations

The Attempt at a Solution

I don't quite understand what they're asking.. I know that at a point, all of the coordinates of the points on line L will be negative. But are they asking us to simply find a vector from the origin to the point at which this happens? Or are they asking us to find a vector along the line that represents all of these points (which doesn't make sense to me because in my mind that vector would be infinitely long).

Thanks!

 

[HmBe]

Could it just be a restriction on t?

 

[skyturnred]

I was actually thinking that too.. but it seems too simple to be worth 4 points in my assignment.

 

[SammyS]

Is it standard practice to parametrize the segment so that when the scalar parameter spans the interval [0, 1], the vector parametrization spans the entire segment ?