(b) The path of a moving body is defined by r(t) = costi+ sint j + (2 - sint)k. (i) Show that the path is the curve of intersection of the cylinder x² + y² = 1 and the plane y + z = 2 and use this fact to sketch the curve. (ii) Find and sketch the position and velocity vector at t = as in (i). on the same diagram
(b) The path of a moving body is defined by r(t) = costi+ sint j + (2 - sint)k. (i) Show that the path is the curve of intersection of the cylinder x² + y² = 1 and the plane y + z = 2 and use this fact to sketch the curve. (ii) Find and sketch the position and velocity vector at t = as in (i). on the same diagram
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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Solve b
Transcribed Image Text:(b) The path of a moving body is defined by r(t) = costi+ sint j + (2 - sint)k.
(i) Show that the path is the curve of intersection of the cylinder x² + y² = 1 and
the plane y + z = 2 and use this fact to sketch the curve.
(ii) Find and sketch the position and velocity vector at t = π on the same diagram
(4 m)
as in (i).
x² - y²
x² + y²
(i) In which direction should you move froma the point (1,
maximum increase of f?
(ii) Find the direction in which the directional derivative at the poin
to zero.
(c) Let f(x, y)
=
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