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Section 6 Wrap Up Questions

  1. Describe graphically what a curl-free vector field looks like.

  2. Describe graphically what a divergence-free vector field looks like. Note: A divergence-free vector field has \(0\) divergence at all points.

  3. Are the following statements true or false? Give reasons for your answers.

    • It is not possible to have a vector field that is both curl-free and divergence-free.

    • The two-dimensional scalar curl coincides with the \(\vec{k}\) component of the three-dimensional curl.

    • If \({\rm div} \vec{F} (0,0)=0\text{,}\) then no vectors in \(\vec{F}\) point into the origin.

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