If A and B are two given vectors and what is the procedure to find A.▽B and A x ▽B at a given point?

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This is what I did:

  1. Calculated ▽B and substituted the value of the point to find a vector

  2. Calculated A at the given point by substituted the coordinates in the vector

  3. Dot product of the two to find a vector (final ans)

Is this the right way?

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Yes 1)-3), and 4) Calculate vector product to find $\bf{A}\times\nabla\bf{B}$.