# Let $\mathbf{I}, \mathbf{J},$ and $\mathbf{K}$ are unit vectors along the three mutually perpendicular $x, y$ and $z$ axes, respectively. If $\mathbf{F}=\mathrm{fI}+\mathrm{g} \mathbf{J}+\mathrm{h} \mathbf{K}$ is a continuously differentiable vector point function, then $\mathbf{c u r l} \mathbf{F}$ is (A) $\mathbf{I}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{y}}\right)-\mathrm{J}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{x}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{x}}\right)$ (B) $\mathbf{I}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{z}}\right)-\mathrm{J}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{z}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\right)$ (C) $\mathbf{I}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{z}}\right)+\mathrm{J}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{z}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\right)$ (D) $\mathbf{I}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{y}}\right)+\mathrm{J}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{x}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{x}}\right)$

## Question ID - 156902 | Toppr Answer Let $\mathbf{I}, \mathbf{J},$ and $\mathbf{K}$ are unit vectors along the three mutually perpendicular $x, y$ and $z$ axes, respectively. If $\mathbf{F}=\mathrm{fI}+\mathrm{g} \mathbf{J}+\mathrm{h} \mathbf{K}$ is a continuously differentiable vector point function, then $\mathbf{c u r l} \mathbf{F}$ is (A) $\mathbf{I}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{y}}\right)-\mathrm{J}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{x}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{x}}\right)$ (B) $\mathbf{I}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{z}}\right)-\mathrm{J}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{z}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\right)$ (C) $\mathbf{I}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{z}}\right)+\mathrm{J}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{z}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\right)$ (D) $\mathbf{I}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{y}}\right)+\mathrm{J}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{z}}-\frac{\partial \mathrm{h}}{\partial \mathrm{x}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{f}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{x}}\right)$

(B) $\mathbf{I}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{y}}-\frac{\partial \mathrm{g}}{\partial \mathrm{z}}\right)-\mathrm{J}\left(\frac{\partial \mathrm{h}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{z}}\right)+\mathrm{K}\left(\frac{\partial \mathrm{g}}{\partial \mathrm{x}}-\frac{\partial \mathrm{f}}{\partial \mathrm{y}}\right)$