Let's analyze the Assertion (A) and the Reason (R) separately to determine their truth values and relationship.

Assertion (A): "Curl of any vector is a vector. It gives a normal vector which is perpendicular to both the plane and the parent vector."

• The curl of a vector field is indeed another vector field. It is defined in vector calculus and is used to describe the rotation of a vector field.
• The curl is perpendicular to the surface defined by the vector field and a normal vector to it is indeed part of its properties.
• Thus, the assertion is correct since the curl provides a direction normal to the plane formed by the parent vector components.

Reason (R): "The value of curl of H can be found by the expression: \((\text{Curl H})_{\text{Normal}} = \lim_{\Delta S\to0}\dfrac{\oint \vec{H}\cdot d\vec{l}}{\Delta S}\)"

• This expression is a direct application of Stokes' Theorem from vector calculus. It relates the curl of a vector field to a line integral around a closed loop.
• This definition accurately describes how to compute the curl using the limit of a surface integral, confirming the mathematical approach, so the reason is also correct.

Relation between Assertion (A) and Reason (R):

• While both the assertion and the reason are true, the expression given in the reason is a mathematical formulation used to calculate the curl, not an explanation of why the curl is a vector that is perpendicular to the plane and the parent vector.
• Therefore, although both statements are correct, the reason does not serve as the direct explanation for the assertion, making option 2 the correct choice.

Therefore, the correct option is: Both (A) and (R) are true, but (R) is not the correct explanation of (A).