Consider the plane z = x + 2y and the cylinder x^2 + y^2 = 1
(a) Find a vector function r(t) describing their intersection.
(b) Find the points if any where the tangent to ~r is horizontal
(c) Find an equation for the tangent line to ~r at each of these points.
The Attempt at a Solution
r(t) = cos(t)i+sin(t)j+(cos(t)+2sin(t))k
r'(t) = -sin(t)i + cos(t)j + (-sin(t)+2cos(t))k
These equations are correct, as I have plotted them in Maple 14 and the images appear correct. I'm having issues finding the horizontal tangent, and then finding the equations afterwards.
The horizontal tangent should be when r'(t) = 0 correct? I cannot find a value that makes this true. Maybe I'm making a mistake in my thinking?
Thank you for any help.