Calc 3 worksheet must be done in 2 hours

NAME:

Worksheet Two : Vector Valued Functions

1. Find the parametric equations for the following curves: A. The line segment from P = (9, 8, 5) to Q = (13,−2, 0).

B. x2 + y2 = 9 for only positive x values.

2. Find the vector valued function describing the curves of intersection of the pairs of surfaces. Then draw the two surfaces together in the space provided.

A. The parabaloid y = x2 + z2 and the parabolic cylinder z = x2.

y

z

x

B. The cylinder x2 + y2 = 1 and the parabolic cylinder z = x2.

y

z

x

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3. If a particle has an initial position of ~r(0) = î − 2ĵ and its velocity is given by the vector function ~v(t) = 〈2e2t, 3t2 − 1, t3〉, find the particles position function and acceleration function.

4. Find the tangent line to the curve ~r(t) = ⟨ 3 ln(t), 2t− 3, 1

t

⟩ at t = 1.

5. If a particle follows the path defined by ~r(t) = 〈2t3/2, 2t + 1, √

5t〉 and starts at t = 0, at what time will the particle have traveled a total of 14 units?

6. Let ~r(t) = 〈t, t, 2 − t2〉. Find the curvature when t = 0, denoted by κ(0).

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