Question

The value of the constant \(a\) so that the vector \[ \vec{V}=(x+3y)\hat{i}+(y-2z)\hat{j}+(x+az)\hat{k} \] is solenoidal is

• A. \(-1\)
• B. \(1\)
• C. \(-2\)
• D. \(2\)

Hint:

A vector field is \[ \boxed{\text{Solenoidal} \iff \nabla\cdot\vec{V}=0.} \] Always compute \[ \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y} + \frac{\partial R}{\partial z}. \]

Answer 1

The Correct Option is C