All parts pls (7) If F(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is a vector field on R3and the partial derivatives of P(x, y, z), Q(x, y, z), and R(x, y, z) all exist, then thecurl of F is the vector field on R³ defined byOP'მი(OP-OR).əx дуand the divergence of F is the function of three variables defined bycurl F=(ORaQƏzi+ӘР ƏQdiv F(x,y,z)= + +Ər дуSolve the following problems.ᎧᎡəzj+kI(a) A vector field F(x,y,z) is irrotational if curl(F) is equal to zero. Find constantsa, b, c so that F = (x+2y+az)i + (br - 3y - z)j + (4x+cy + 2z)k is irrotational.(b) Show that F = (6ry + z³)i + (3r² − z)j + (3xz2 - y)k is irrotational.(c) A vector field F(x,y,z) is soleinoidal if its divergence is zero. Is F = (3y¹22)i +(4x³2²)j + (-3r²y²)k soleinoidal?

For irrotational curl F=0 F=Pi+Qj+RkCurl F=∇×F=ijk∂∂x∂∂y∂∂zPQR…

(7) If F(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is a vector field on R³ and the partial derivatives of P(x, y, z), Q(x, y, z), and R(x, y, z) all exist, then the curl of F is the vector field on R³ defined by ӘР curl F- (-22) + (-32) ₁+ (2) ► F= j+ k ду Əz and the divergence of F is the function of three variables defined by ӘР ƏQ OR div F(x,y,z)= + + əx ду Solve the following problems. I (a) A vector field F(x,y,z) is irrotational if curl(F) is equal to zero. Find constants a, b, c so that F = (x+2y+az)i + (br - 3y - 2)j + (4x+cy + 2z)k is irrotational. (b) Show that F = (6ry + z³)i + (3x² − z)j + (3xz2 - y)k is irrotational. - (c) A vector field F(x,y,z) is soleinoidal if its divergence is zero. Is F = (3y¹22)i + (1r³2²)j + (-3r²y²)k soleinoidal?

(7) If F(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is a vector field on R³ and the partial derivatives of P(x, y, z), Q(x, y, z), and R(x, y, z) all exist, then the curl of F is the vector field on R³ defined by ӘР curl F- (-22) + (-32) ₁+ (2) ► F= j+ k ду Əz and the divergence of F is the function of three variables defined by ӘР ƏQ OR div F(x,y,z)= + + əx ду Solve the following problems. I (a) A vector field F(x,y,z) is irrotational if curl(F) is equal to zero. Find constants a, b, c so that F = (x+2y+az)i + (br - 3y - 2)j + (4x+cy + 2z)k is irrotational. (b) Show that F = (6ry + z³)i + (3x² − z)j + (3xz2 - y)k is irrotational. - (c) A vector field F(x,y,z) is soleinoidal if its divergence is zero. Is F = (3y¹22)i + (1r³2²)j + (-3r²y²)k soleinoidal?

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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