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Calculus and Beyond Homework Help
How to find which of three points are on a line?
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[QUOTE="brmath, post: 4502036, member: 486151"] First, you are right that P and Q fall on the line and R does not. And as you see, R is not on the line because using those points you get 3 incompatible equations in t. Whether a point falls on a line depends on all 3 magnitudes, i, j and k, and the trivial answer to your question is that most combinations will not work i.e. most 3 dimensional points are not on any given line. However, working backwards from the equation we can get some insight. For example r(0) = i + 2j. So the point that fits there is P = (1,2,0). When you look at r(-1) = -5i + j - 5k, you see that Q = (-5,1,-5) is a point on the line. But your incompatible equation for R tells you that there is no possible t for which r(t) = R. It's not really deeper than that. [/QUOTE]
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How to find which of three points are on a line?
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