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Math 2210 Problem Set 4, Key Problem 1 Either find the plane containing the following curves or demonstrate that
 

Summary: Math 2210 Problem Set 4, Key
Problem 1 Either find the plane containing the following curves or demonstrate that
no such plane exists.
(i) (t2
, 1 - t2
, 2t + 3),
(ii) (Cos(t), Sin(t), t + 2))
Solution 1(i)
Find three points:
t name point
0 P (0,1,3)
1 Q (1,0,5)
-1 R (1,0,1)
Compute two vectors in the plane from these points: RP = (-1, 1, 2) and RQ =
(0, 0, 4) so a normal vector is RP RP = (4, 4, 0) yielding the plane
4(x - 1) + 4(y - 0) + 0(z - 1) = 0
or
4x + 4y - 4 = 0
Solution 1(ii)
Notice this curve is a spiral centered on the z axis. This means it contains an

  

Source: Ashlock, Dan - Department of Mathematics and Statistics, University of Guelph

 

Collections: Mathematics