Curl of vector overrightarrow rm F = rm x ^2 rm...

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Curl of vector \[\overrightarrow {\rm{F}} = {{\rm{x}}^2}{{\rm{z}}^2}{\rm{\hat i}} - 2{\rm{x}}{{\rm{y}}^2}{\rm{z\hat j}} + 2{{\rm{y}}^2}{{\rm{z}}^3}{\rm{\hat k}}\] is

A. \[\left( {4{\rm{y}}{{\rm{z}}^3} + 2{\rm{x}}{{\rm{y}}^2}} \right){\rm{\hat i}} + 2{{\rm{x}}^2}{\rm{z\hat j}} - 2{{\rm{y}}^2}{\rm{z\hat k}}\]

B. \[\left( {4{\rm{y}}{{\rm{z}}^3} + 2{\rm{x}}{{\rm{y}}^2}} \right){\rm{\hat i}} - 2{{\rm{x}}^2}{\rm{z\hat j}} - 2{{\rm{y}}^2}{\rm{z\hat k}}\]

C. \[2{\rm{x}}{{\rm{z}}^2}{\rm{\hat i}} - 4{\rm{xyz\hat j}} + 6{{\rm{y}}^2}{{\rm{z}}^2}{\rm{\hat k}}\]

D. \[2{\rm{x}}{{\rm{z}}^2}{\rm{\hat i}} + 4{\rm{xyz\hat j}} + 6{{\rm{y}}^2}{{\rm{z}}^2}{\rm{\hat k}}\]

Answer: Option A

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