If
\[
\vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k},
\]
then the value of
\[
\vec{v}\cdot(\nabla\times\vec{v})
\]
is
Show Hint
To solve questions involving curl and dot product:
• First identify the components \(P\), \(Q\), and \(R\).
• Compute the curl using the determinant formula.
• Finally, evaluate the dot product using
\[
\vec{A}\cdot\vec{B}=A_xB_x+A_yB_y+A_zB_z.
\]
• Always simplify completely before selecting the option.