Worksheet: Divergence and Curl in Cartesian Coordinates

In this worksheet, we will practice finding the divergence and the curl of a vector field in Cartesian coordinates and discussing their physical meaning.

Q1:

Which of the following is true concerning the vector field V defined by Vik(𝑥,𝑦,𝑧)=𝑦𝑥?

  • AV(𝑥,𝑦,𝑧) is orthogonal to the vector j0,1,0, for all (𝑥,𝑦,𝑧).
  • BV(𝑥,𝑦,𝑧)0, for all (𝑥,𝑦,𝑧).
  • CV has a positive divergence at every point (𝑥,𝑦,𝑧).
  • DV is a conservative vector field.

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