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SSC Pure Mathematics QUESTION #11134
Question 1
The vector field $\mathbf{V} = (-4x-6y+3z)\,\mathbf{i} + (-2x+y-5z)\,\mathbf{j} + (5x+6y+az)\,\mathbf{k}$ is solenoidal for $a=$
  • $1$
  • $2$
  • $3$✔️
  • $4$
Correct Answer Explanation
For a solenoidal field, $\nabla \cdot \mathbf{V} = 0$. Computing: $\dfrac{\partial}{\partial x}(-4x-6y+3z) + \dfrac{\partial}{\partial y}(-2x+y-5z) + \dfrac{\partial}{\partial z}(5x+6y+az) = -4 + 1 + a = 0$. Therefore $a - 3 = 0$, giving $\boxed{a = 3}$.