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Question 3 [20 marks] a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?. If A = 2y î ? z ? + 3x k? (i) Find the unit vectors ê_r, ê_? and ê_? of a spherical coordinate system in terms of î, ? and k?. [6 marks] (ii) Solve for î, ? and k? in terms of ê_r, ê_? and ê_?. [3 marks] (iii) Prove that the spherical coordinate system is orthogonal. [3 marks] (iv) Represent the vector A in spherical coordinates and determine A_r, A_? and A_?. [4 marks]

          Question 3 [20 marks]

a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?. If A = 2y î ? z ? + 3x k?

(i) Find the unit vectors ê_r, ê_? and ê_? of a spherical coordinate system in terms of î, ? and k?. [6 marks]

(ii) Solve for î, ? and k? in terms of ê_r, ê_? and ê_?. [3 marks]

(iii) Prove that the spherical coordinate system is orthogonal. [3 marks]

(iv) Represent the vector A in spherical coordinates and determine A_r, A_? and A_?. [4 marks]

Question 3 [20 marks]

a. In spherical coordinates x = r sin ? cos ?, y = r sin ? sin ? and z = r cos ?. If A = 2y î ? z ? + 3x k?

(i) Find the unit vectors êr, ê? and ê? of a spherical coordinate system in terms of î, ? and k?. [6 marks]

(ii) Solve for î, ? and k? in terms of êr, ê? and ê?. [3 marks]

(iii) Prove that the spherical coordinate system is orthogonal. [3 marks]

(iv) Represent the vector A in spherical coordinates and determine Ar, A? and A?. [4 marks]

Added by Virginia P.

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