Question

If \({\rm{F}}\) is a vector field, then curl \({\rm{F}}\) is a vector field.

Short answer

The given statement is true

Step-by-step solution

Curl \({\rm{F}}\)is also a vector field.

True. Curl \({\rm{F}}\) is also a vector field if \({\rm{F}}\) is a vector field by definition. Moreover, if \({\rm{F = Pi + Qj + Rk}}\).

Explanation of true statement.

Then, it is written as

\(\)\({\rm{curlF = }}\left( {\frac{{\partial R}}{{\partial y}} - \frac{{\partial Q}}{{\partial z}}} \right){\rm{i + }}\left( {\frac{{\partial P}}{{\partial z}} - \frac{{\partial R}}{{\partial x}}} \right){\rm{j + }}\left( {\frac{{\partial Q}}{{\partial z}} - \frac{{\partial P}}{{\partial y}}} \right){\rm{k}}\)

Hence, the given statement is true.