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a) A three dimensional motion of an object is given by the vector function r(t) = 4 cost i+ 4sin tj +5 k. 37 and the velocity Sketch the motion of the object when 0

a) A three dimensional motion of an object is given by the vector function r(t) = 4 cost i+ 4sin tj +5 k. 37 and the velocity Sketch the motion of the object when 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 34RE
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a) A three dimensional motion of an object is given by the vector function r(t) = 4 cos t i+ 4 sin tj+5 k. Sketch the motion of the object when 0<ts 37 and the velocity vector of the object when t . b) Let F(r, y, 2) = sin 2r i+ rz cos yj+ey k. Then find i. div F, ii. curl F, ii. V (V.F). c) Given a function O(x, y, z) = 3x + In (3y + 1) +e* cos z. i. Find the directional derivative of o at (0, 1, 7) in the direction of a = 4i – 2j + 4k. ii. Find the minimum directional derivative of o and its direction at (0, 1, 7).
Transcribed Image Text:a) A three dimensional motion of an object is given by the vector function r(t) = 4 cos t i+ 4 sin tj+5 k. Sketch the motion of the object when 0<ts 37 and the velocity vector of the object when t . b) Let F(r, y, 2) = sin 2r i+ rz cos yj+ey k. Then find i. div F, ii. curl F, ii. V (V.F). c) Given a function O(x, y, z) = 3x + In (3y + 1) +e* cos z. i. Find the directional derivative of o at (0, 1, 7) in the direction of a = 4i – 2j + 4k. ii. Find the minimum directional derivative of o and its direction at (0, 1, 7).
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