Question

Question 3[20 marks] a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?. If A = 2yi? - zj? + 3xk? (i). Find the unit vectors êr, ê? and ê? of a spherical coordinate system in terms of î, ? and k?. (ii). Solve for î, ? and k? in terms of êr, ê? and ê? (iii). Prove that the spherical coordinate system is orthogonal (iv). Represent the vector A in spherical coordinates and determine Ar, A? and A?

          Question 3[20 marks]
a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?.
If A = 2yi? - zj? + 3xk?
(i). Find the unit vectors êr, ê? and ê? of a spherical coordinate system in terms of î, ? and k?.
(ii). Solve for î, ? and k? in terms of êr, ê? and ê?
(iii). Prove that the spherical coordinate system is orthogonal
(iv). Represent the vector A in spherical coordinates and determine Ar, A? and A?

Question 3[20 marks]
a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?.
If A = 2yi? - zj? + 3xk?
(i). Find the unit vectors êr, ê? and ê? of a spherical coordinate system in terms of î, ? and k?.
(ii). Solve for î, ? and k? in terms of êr, ê? and ê?
(iii). Prove that the spherical coordinate system is orthogonal
(iv). Represent the vector A in spherical coordinates and determine Ar, A? and A?

Added by Luz J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/27/2023

Step 1

(i) Show more…

Show all steps

Thanks for your feedback!

Question 3[20 marks] In spherical coordinates x = r sin θ cos φ, y = r sin θ sin φ and z = r cos θ. If A = 2yi - zj + 3xk (i). Find the unit vectors êr, êθ and êφ of a spherical coordinate system in terms of î, ĵ and k̂. (ii). Solve for î, ĵ and k̂ in terms of êr, êθ and êφ (iii). Prove that the spherical coordinate system is orthogonal (iv). Represent the vector A in spherical coordinates and determine Ar, Aθ and Aφ