Multi-Variable Calculus Assignment

due Friday, February 16, 2001

Exercises

1. Find the angle between the twisted cubics

   s -> (s, s^{2}, s^{3}) and t -> (t^{2}, t^{3}, t)

   at the point (1, 1, 1).

2. Find the angle between the line

   t ---> (1 - 2t, -3 + t, 2 - t)

   and the plane x + y + z = 0.

3. Find the angle between the two planes

   x - 2y + z = 2 and 2x - 3y - z = 1 .

4. Let a > 0 and b be given constants, and let F be the parameterized helix

   F(t) = (-a sin t, a cos t, b t) .

   Let gamma be the function defined by the statement that gamma(t) is the arc length along the helix from the point F(0) to the point F(t).

   Find a formula for gamma(t).

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