Vorticity of a vector field

is defined as

Given

 = kxyz î, where k is a constant, which one of the following is correct?​

Correct option is D

Solution:

Analyze the options:

• Option (a): "Vorticity is a null vector for all finite x, y, z"
  This is incorrect because the curl is not zero.

• Option (b): "Vorticity is parallel to the vector field everywhere"
  This is incorrect because the curl of a vector field is always perpendicular to the original vector field.

• Option (c): "The angle between vorticity and vector field depends on x, y, z"
  This is incorrect because the angle between the curl and the original field is always 90 degrees.

• Option (d): "Vorticity is perpendicular to the vector field everywhere"
  This is correct because the vorticity vector is always perpendicular to the original vector field for this calculation.