Hello, I have a "graphical" problem. Let's say you have two points, 1 and 2, with some initial position. Let's make the initial position vectors r10 and r20. Let the points have constant velocity vectors v1 and v2. This gives, as a function of time,
r1(t) = r10 + v1*t
r2(t) = r20 + v2*t
The problem is to find at what time t the line segment between the two points intersects the origin. I had two approaches to this problem - The first, I made a line between the two points which changes with time and inserted x = 0 and y = 0 into the line's equation.
This gave me another equation. In addition to the four equations from the vectors (2 for each from x and y), I have 5 equations, and 5 unknowns (r1, r2, and t - r1 and r2 have two unknowns each). Solving for t using Mathematica gave me one very long answer. So that solution I'm confident in. Then, I tried a different approach. I made a conjecture that if r1(t)/|r1(t)| =-r2(t)/|r2(t)| then the two position vectors must be parallel and therefore intersect the origin with the line segment. Sounds good, right? However, solving this one equation for t gave a completely different answer than that of the previous solution... And there's where I'm stuck.
@telliott99 No I need to solve symbolically.

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Do you have actual values? Maybe a diagram will help...

Sorry, but I gotta go. Great problem.

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