Curl of Vector Field u = yi+(x+z)j+xy^(2)k: Step-by-Step Calculation Method

[andrey21]

Find the curl of the following vector field

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

Now using the method I've 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.

 

[Char. Limit]

Confirmed that it is correct, then.

 

[andrey21]

Thank you Char.limit just a follow up question I am asked:

Find (curl u).v

Where
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

 

[Char. Limit]

Yes it is. And you can just ignore the k part completely.

 

[andrey21]

So would that give me:

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

Also do I still need the i j k notations??

 

[dextercioby]

YOu have obtained a scalar. There's no more unit vector involved.

 

[andrey21]

Oh ok so my final answer would just be 2x^(2) - x +y^(4) - y^(2)

correct?