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Let $u = x + y + z, v = x^{2} + y^{2} + z^{2}, w = yz + zx + xy$. Then the vectors $\nabla u, \nabla v, \nabla w$ are}

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If a functional relationship exists between $u, v,$ and $w$, their gradients will always be coplanar (linearly dependent).

Updated On: Jul 3, 2026

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