Determine the parametric equations for the line that passes through the two points A=(4, -1, 5) and B= (3, 5, -1).
At what point does this line intersect the x-y plane
As you know a line equation in has the following form:
where is a point that line passes through, and is a vector that is parallel to the line.
Returning to your problem, we have a point that the desired line passes through (we may pick or ), but we need the vector .
We may let as vector, try to see that the line will be parallel to .
Thus, the line is
To find the value that line intersects -plane, we have to set the third component (height) of the line to and solve .
I hope you can find it now?