Match List-I with List-II

List - I

List - II

(A)

The unit normal to the surface x³ - xyz + z³ = 1 at (1, 1, 1)

(I)

\(\hat{k}\)

(B)

If \(\phi=\frac{y}{x^2+y^2},\left.(\nabla \phi)\right|_{(1,0)}\) =

(II)

\(\hat{j}\)

(C)

If \(\vec{F}=x^2 \hat{i}+2 z^2 \hat{j}-\left.3 y^2 \hat{k}_t(\nabla \times \vec{F})\right|_{(0,-1,-1)}\)

(III)

10\(\hat{i}\)

(D)

If \(\phi=\frac{y}{x^2+y^2},\left.(\nabla \phi)\right|_{(0,1)} \times \hat{i}=\)

(IV)

\(\frac{1}{3}(2 \hat{i}-\hat{j}+2 \hat{k})\)

Choose the correct answer from the options given below:

Question

List - I		List - II
(A)	The unit normal to the surface x³ - xyz + z³ = 1 at (1, 1, 1)	(I)	\(\hat{k}\)
(B)	If \(\phi=\frac{y}{x^2+y^2},\left.(\nabla \phi)\right\|_{(1,0)}\) =	(II)	\(\hat{j}\)
(C)	If \(\vec{F}=x^2 \hat{i}+2 z^2 \hat{j}-\left.3 y^2 \hat{k}_t(\nabla \times \vec{F})\right\|_{(0,-1,-1)}\)	(III)	10\(\hat{i}\)
(D)	If \(\phi=\frac{y}{x^2+y^2},\left.(\nabla \phi)\right\|_{(0,1)} \times \hat{i}=\)	(IV)	\(\frac{1}{3}(2 \hat{i}-\hat{j}+2 \hat{k})\)