দেওয়া আছে, $\vec{V} = (x + y + az)\hat{i} + (bx + 3y - z)\hat{j} + (3x + cy + z)\hat{k}$ ভেক্টরটি অঘূর্ণনশীল হলে, $\nabla \times \vec{V} = 0$ হবে। $$ \begin{aligned} \nabla \times \vec{V} &= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ x+y+az & bx+3y-z & 3x+cy+z \end{vmatrix} \\ &= \hat{i} \left( \frac{\partial}{\partial y}(3x+cy+z) - \frac{\partial}{\partial z}(bx+3y-z) \right) - \hat{j} \left( \frac{\partial}{\partial x}(3x+cy+z) - \frac{\partial}{\partial z}(x+y+az) \right) + \hat{k} \left( \frac{\partial}{\partial x}(bx+3y-z) - \frac{\partial}{\partial y}(x+y+az) \right) \\ &= \hat{i} (c - (-1)) - \hat{j} (3 - a) + \hat{k} (b - 1) \\ &= \hat{i} (c + 1) + \hat{j} (a - 3) + \hat{k} (b - 1) \end{aligned} $$ শর্তমতে, $\nabla \times \vec{V} = 0$ হলে, $$ \begin{aligned} c + 1 &= 0 \Rightarrow c = -1 \\ a - 3 &= 0 \Rightarrow a = 3 \\ b - 1 &= 0 \Rightarrow b = 1 \end{aligned} $$ অতএব, $a=3, b=1, c=-1$।