Cylindrical coordinates (p, ó, z): ê, = cos o î + sin ø 3, ês = - sin ø î + cos o ĵ, êz = k (4) (5) COS (6) Spherical coordinates (r, 0, »): ê, = sin 0 cos o î + sin 0 sin ø ĵ + cos 0 k, êg = cos 0 cos o î + cos 0 sin ø ĵ – sin 0 k, ês = - sin o î + cos j. (7) (8) (9) a) Find the expressions of (êr, êo, ês) in terms of (êp, êp, êz). b) A vector can be expressed in terms of any basis. In particular, we can write: V = V,êp + V,êy + V,ê; = V,êp + Vyês + Vyê; = V,ê, + Voêo + Vgêp. (10) %3D In terms of column vector notation we write

Cylindrical coordinates (p, ó, z): ê, = cos o î + sin ø 3, ês = - sin ø î + cos o ĵ, êz = k (4) (5) COS (6) Spherical coordinates (r, 0, »): ê, = sin 0 cos o î + sin 0 sin ø ĵ + cos 0 k, êg = cos 0 cos o î + cos 0 sin ø ĵ – sin 0 k, ês = - sin o î + cos j. (7) (8) (9) a) Find the expressions of (êr, êo, ês) in terms of (êp, êp, êz). b) A vector can be expressed in terms of any basis. In particular, we can write: V = V,êp + V,êy + V,ê; = V,êp + Vyês + Vyê; = V,ê, + Voêo + Vgêp. (10) %3D In terms of column vector notation we write

Name: Question 2:Three frequently used coordinates in R³ are 1: Cartesian C
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Description: Question 2:Three frequently used coordinates in R³ are 1: Cartesian Coordinates, 2: Cylindrical coordi-nates, and 3: Spherical Coordinates. Unit vectors in these coordinates are the following.Cartesian coordinates (r, y, z):êz = î,êy = 3,ê̟ = k.(1)(

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 43E

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