Dimension of Quotient Subspace If W is a subspace of a vector space V over z3 BHU PET 2018 maths

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Linear Algebra: Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions, eigenvalues, and eigenvectors for matrices, Cayley-Hamilton theorem.

En BHU PET 2018, 7
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Please someone help me with this question:
Let X be a subset of R³ and let:
V = { F | F: (R³−X) −→ R³ com rot(F) = 0 },
W = { F | F: (R³−X) −→ R³ com F = grad(g) }Find the dimension of the vector space quotient V /W.

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