Consider F(r,o, z) = 0³ē, +4rē + 3r²ze, and 3r2 222 i. What are the Lamé coefficients for cylindrical polar coordinates? ii. State the expression for the gradient of in cylindrical polar coordi- nates and evaluate for given above. iii. State the expression for the Laplace operator acting on in cylindri- cal polar coordinates and evaluate for given above. iv. State the expression for the divergence of F in cylindrical polar co- ordinates and evaluate for F given above. Note: You may make use of the following formula for a general curvi- linear coordinate system if you need to: -ei+ -e2+· 1 მს 1 მს 1 მს իլ Օզի h₂ 92 hვ მყვ -ē3. V.F [ ǝ(hahaF¹)¸ǝ(hṛhaF2) Ə(hıh¸Fs) VÝ 1 + = h₁h2h3 aq2 მივ h₁e he hзe3 1 V × F= მ 8 მ h₁h2h3 Օգ 892 ддз Fihi F2h2 F3h3 1 მ h2h3 მს მ hha მს 12√ + = h₁h2h3 91 իլ Օզլ მ42 հ2 Օզչ მ hh2 მს + მ43 h3 93.