Lec 5 | MIT 18.02 Multivariable Calculus, Fall 2007
Lecture 05: Parametric equations for lines and curves. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More ...
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So -- So, yesterday we learned about the questions of planes and how to think of 3x3 linear systems in terms of intersections of planes and how to think about them geometrically. And, that in particular led us to see which cases actually we don't have a unique solution to the system, but maybe we have no solutions or infinitely many solutions because maybe the line at intersection of two of the planes happens to be parallel to the other plane. So, today, we'll start by looking at the equations of lines. And, so in a way it seems like something which we've already seen last time because we have seen that we can think of a line as the intersection of two planes. And, we know what equations of planes look like. So, we could describe a line by two equations telling us about the tw...
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So -- So, yesterday we learned about the questions of planes and how to think of 3x3 linear systems in terms of intersections of planes and how to think about them geometrically. And, that in particular led us to see which cases actually we don't have a unique solution to the system, but maybe we have no solutions or infinitely many solutions because maybe the line at intersection of two of the planes happens to be parallel to the other plane. So, today, we'll start by looking at the equations of lines. And, so in a way it seems like something which we've already seen last time because we have seen that we can think of a line as the intersection of two planes. And, we know what equations of planes look like. So, we could describe a line by two equations telling us about the tw...
