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Math20_Fall2011_linesandplanesSolutions

Math20_Fall2011_linesandplanesSolutions - Harvard...

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Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein 1 Lines and Planes September 16, 2011 Find the following line and planes, using either parametric form or an equa- tion. Let P = (1 , 2 , 3 , 4), Q = (2 , 3 , 4 , 4), and R = (0 , 0 , 2 , 0). 1. Find the line through the points P and Q . This line is the set: { Qt + P (1 - t ) | t R } . This is the same as the set 1 + t 2 + t 3 + t 4 | t R There are other right answers to this problem. To check your answer, see if you can choose t in such a way that you recover the points P and Q . For the answer above, choosing t = 0 and t = 1 works. 2. Find the plane through the points P , Q , and R . This is a bit harder, since we didn’t specifically do an example like this in class. We must first convert it to a problem that says, “Find the plane through P , parallel to vectors ~v and ~w .” But what should ~v and ~w be? We can use the vectors ~ PQ and ~ PR , or any other vector through two points on the plane.

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Math20_Fall2011_linesandplanesSolutions - Harvard...

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