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Let the functions $u$ and $v$ be differentiable functions of $x$, $y$ and $z$. Show that a necessary and sufficient condition that $u$ and $v$ are functionally related by the equation $F(u,v)=0$ is

  1. $\bigtriangledown u \times \bigtriangledown v =0$
  2. $\bigtriangledown u . \bigtriangledown v =0$
  3. Both A and B
  4. None of the above
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