3. (a) Given the vector valued function r(t) = 4 cos zti + 4 sin atj + tk. Find the position vector, the unit tangent vector T(t) and the unit normal vector N(t) at t= 1. (b) Given F(z, yz) = 3ry'i + yzj + zr*k and o(r, y, 2) = re" sin y. Calculate i. curl curl F ii. V (Vo) (c) The temperature in degrees celcius at a point (r, y, 2) in a metal solid is ryz T(1, y, 2) = 1+r² + y² + z²° Find the rate of change at the point (1,1, 1) towards the origin.
3. (a) Given the vector valued function r(t) = 4 cos zti + 4 sin atj + tk. Find the position vector, the unit tangent vector T(t) and the unit normal vector N(t) at t= 1. (b) Given F(z, yz) = 3ry'i + yzj + zr*k and o(r, y, 2) = re" sin y. Calculate i. curl curl F ii. V (Vo) (c) The temperature in degrees celcius at a point (r, y, 2) in a metal solid is ryz T(1, y, 2) = 1+r² + y² + z²° Find the rate of change at the point (1,1, 1) towards the origin.
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:3. (a) Given the vector valued function r(t) = 4 cos rti + 4 sin rtj + tk.
Find the position vector, the unit tangent vector T(t) and the
unit normal vector N(t) at t= 1.
(b) Given F(r, yz) = 3ry'i + yzj + zrk and o(x, y, 2) = re" sin y.
Calculate
i. curl curl F
ii. V. (Vo)
(c) The temperature in degrees celcius at a point (r, y, 2) in a metal
solid is
ryz
T(r,y, 2) =:
1+ 12 + y² + z²°
Find the rate of change at the point (1, 1, 1) towards the
origin.
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