Multiple choice

$\nabla$ × P, where P is a vector, is equal to

  1. Px $\nabla$ x P − $\nabla^2$P
  2. $\nabla^2$P + $\nabla$($\nabla$.P)
  3. $\nabla^2$P + $\nabla$x P
  4. $\nabla$($\nabla$.P) - $\nabla^2$P
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\text{The vector Triple product is} \\ A \times (B \times C) = B(A.C) - C(A.B) \\ Thus \hspace{0.2cm} \nabla \times \nabla \times P = \nabla(\nabla .P) P(\nabla.\nabla) = \nabla(\nabla . P) - \nabla^2 P$

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