Math 2210 Section 1 - Spring 2008
Exam I
Answer the questions in the spaces provided on the question sheets. Show all
work to receive credit. Calculators are not permitted. Each question is worth
10 points.
Name:
1
2
1. Find the arc length of the curve given by
x = t, y = −2t, z = 3t; −1 ≤ t ≤ 1.
3
2. Find the cosine of the angle between the vectors a = h1, 1, 2i and b = h−2, 3, −4i.
Find proja b.
4
3. Find an equation for the plane through the points (1, 3, 2), (0, 3, 0) and (2, 4, 3).
5
4. If r(t) = sin 3t i − cos 3t j, find Dt [r(t) · r′ (t)].
6
5. Find the parametric equations of the line through (2, −1, −5) and (7, −2, 3).
7
6. Find the unit tangent vector T and the curvature κ for the curve given by
√
r(t) = e−2t i + e2t j + 2 2tk
at t = 0.
8
7. Rewrite the equation 2x2 + 2y 2 − 4z 2 = 0 in spherical coordinates.