Let F(t) be a vector valued function whose derivative is F'(t) = G(t) = (6t, 3t, −6t). 1. If F(2) = (6, 3, -6), determine F(t). 2. Reparametrize G(t) using the directed arc length from the reference point P(6,3, -6) in the direction of increasing values of t. 3. Determine the coordinates of the point Q on the graph of G such that the directed arc length from P to Q is 9 units.
Let F(t) be a vector valued function whose derivative is F'(t) = G(t) = (6t, 3t, −6t). 1. If F(2) = (6, 3, -6), determine F(t). 2. Reparametrize G(t) using the directed arc length from the reference point P(6,3, -6) in the direction of increasing values of t. 3. Determine the coordinates of the point Q on the graph of G such that the directed arc length from P to Q is 9 units.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:VI. Let F(t) be a vector valued function whose derivative is F'(t) = G(t) = (6t, 3t, −6t).
1. If F(2) = (6,3, -6), determine F(t).
2. Reparametrize G(t) using the directed arc length from the reference point P(6,3, -6)
in the direction of increasing values of t.
3. Determine the coordinates of the point Q on the graph of G such that the directed arc
length from P to Q is 9 units.
VI
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