- #1
Mr Davis 97
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Homework Statement
Let ##A## and ##B## be two given points, ##l## a given line. Find the point ##P## on ##l## such that ##|AP-PB|## is a maximum.
Homework Equations
The Attempt at a Solution
Suppose that the line ##l## and the line that goes through ##A## and ##B## (call it ##\ell_{AB}##) are not parallel. Then our desired point ##P## is the the intersection of ##l## and ##\ell_{AB}##. Is this correct? I'm pretty sure it is.
But what about when ##l## and ##\ell_{AB}## are parallel? There doesn't seem to be a maximum, since if you move a point ##P## along any direction of the line we'll just get greater and greater values for ##|AP-PB|##