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

1 Answer - 5876 Votes

3537

Answer Key : (B) -

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



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