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I have a simple question, but I am unsure. I know from a point p_{0}= (x_{1}, y_{1}) and a vector v = <a, b>, I can obtain a parametrized set of equations for a line in space such that x = x_{1}+ at and y = y_{1}+ bt. How can I check that any other point, not p_{0}, is/isn't in that line?

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# Finding if a point belongs to a line in space.

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