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