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Let $I=\iint_{S}\left(y^{2} z \hat{i}+z^{2} x \hat{j}+x^{2} y \hat{k}\right)[(x \hat{i}+y \hat{j}+z \hat{k}) d S,$ where $S$ denotes the surface of the sphere of unit radius centered at the origin. Here $\hat{i}, \hat{j}$ and $\hat{k}$ denote three orthogonal unit vectors. The value of $I$ is____________



Question ID - 156020 | SaraNextGen Top Answer

Let $I=\iint_{S}\left(y^{2} z \hat{i}+z^{2} x \hat{j}+x^{2} y \hat{k}\right)[(x \hat{i}+y \hat{j}+z \hat{k}) d S,$ where $S$ denotes the surface of the sphere of unit radius centered at the origin. Here $\hat{i}, \hat{j}$ and $\hat{k}$ denote three orthogonal unit vectors. The value of $I$ is____________

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