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Barycentric Vector Equation

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I'm trying to find the exact time of collision between a point and a stationary sphere ((ro)bot). The shot has position = pos and position from previous time step = opos. ||opos + t(opos - pos) - bot.pos|| = bot.radius I've already done a broad phase check and know that the point has indeed collided with the bot between t = 0 and t = 1. I would know what to do if opos, pos, and bot.pos were scalars, but since they're vectors things get a little tricky. How do I solve this? edit: Here's the above written as barycentric equation: ||u(opos) + v(pos) - bot.pos|| = bot.radius where u + v = 1 (obviously ;))

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