Curl And Divergence

(requires JavaScript)

  1. Find the curl and the divergence of the vector field Fxyz=1x+yzxyz .
    xyy1 and z12z
  2. Find the curl and the divergence of the vector field Fxyz=exsinyi+excosyj+zk .
    000 and 1
  3. Let f be a scalar field and F be a vector field. For each of the following expressions, determine whether it is meaningful, and if yes, whether it's a vector or a scalar.

    1. curlf
    2. f
    3. divF
    4. curlf
    5. F
    6. divF
    7. divf
    8. divf
    9. curlcurlF
    10. divdivF
    11. f×divF
    12. divcurlf
  4. Determine whether or not the vector field Fxyz=2xyi+x2+2yzj+y2k is conservative. If it is, find its potential function.
    fxyz=x2y+y2z+K
  5. Determine whether or not the vector field Fxyz=yexi+exj+2zk is conservative. If it is, find its potential function.
    Not conservative.