Curl of a vector field

  1. Find the curl of the following vector field

    u = yi+(x+z)j+xy^(2)k

    Now using the method Ive bin taught similar to finding determinant of 3x3 matrix here is my answer

    i(2yx-1) -j(y^2) +k(0)

    Just looking for confirmation if this is correct or any basic errors I have made thank you.
  2. jcsd
  3. Char. Limit

    Char. Limit 1,937
    Gold Member

    Confirmed that it is correct, then.
  4. Thank you Char.limit just a follow up question I am asked:

    Find (curl u).v

    v = xi+(y^(2) - 1)j+(1-x^(2))k

    Is that just the dot product of the vector v and the curl established for u. Thank you
  5. Char. Limit

    Char. Limit 1,937
    Gold Member

    Yes it is. And you can just ignore the k part completely.
  6. So would that give me:

    (2x^(2) y -x) +(y^(4) - y^(2))

    Also do I still need the i j k notations??
  7. dextercioby

    dextercioby 12,327
    Science Advisor
    Homework Helper

    YOu have obtained a scalar. There's no more unit vector involved.
  8. Oh ok so my final answer would just be 2x^(2) - x +y^(4) - y^(2)

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