Question

Let F 10i4u 8zk. Compute the civergence and curl of F. , div F , curl F Show steps (1 point) Let F (8y2)i(7xz)j+(6y) k Compute the following: A div F В. curl F- i+ k C, div curt F= Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or 5 (1 polnt) Consider the vector field F(r,y, ) = ( 9y , 0, -3ry) Find the divergence and curl of F div(F) VF= curl(F) Vx F ( B) Conskder the vector fleld F(z, y, ) (7x2,-6(z y)2,2(2 +2)2) Find the divergence and curl of F div(F) F- curl(F) Vx F ( (1 point) Let F(7ry, 10y,9). The curl of F Is there a functlon f such that F Vf? (yin) (1 point) 1 Let F 9ri 1zk. Compute the divergence and the curl. A. div F i+ k B. curl F Let F (5ry, 5y, 3z). The curl of F Is there a function f such that F Vf? (yes/no) (1 polnt) For each of the following vector flelds F. decide whether it Is conservative or not by computing curl F. Type in a potentlal function f (that Is, Vf= F). It It is not conservative, type N (16r 3)i(-3z 6y)j A. F (z,y) f(a,) B. F (z, y) 8yi+9xj f(, y) C. F (r, y, 8ri9j k D. F (r,y) (8sin y) i + (-6y + 8r cos y) j (r,y) E. F (z,y,z)8z'i- 3y'j+3z2k f(r,y,z) Note: Your answers should be either expressions of x, y and z fe.g. "3xy + 2yz"), or the letter "N (1 point) Let F be any vector field of the form F f(x)i+g)j (z)k and let G be any vector field of the torm G f(y,)i+g(x,z)jh(x, y) k. Indicate whether the following statements are true or false by placing T" or "F" to the left of the statement 1. G is incompressible .G is Irrotational F is incompressible . F is irrotational

Answer 1

f 10a 4 1. F11 8zK Tab div f + + 으(102) + 유y) ap (82) + 92 - 10+ 4+ 8 22 Curif 92 으(82)-2(102)); (3 (y ) = l0-0)-(0-0j (0-0)k 10n + +OK ald