(1) $$\phi (\alpha )=\left(\begin{array}{c}0\\ \alpha \\ 0\end{array}\right),\alpha \in (-\mathrm{1,1})$$ $$\begin{array}{rl}W& ={\int }_{{\alpha }_1}^{{\alpha }_2}\overrightarrow{F}(\phi (\alpha ))\cdot {\phi }^{\prime }(\alpha )\mathrm{d}\alpha \\ & ={\int }_{-1}^1\left(\begin{array}{c}2{\alpha }^2\\ 0\\ -6{\alpha }^2\end{array}\right)\cdot \left(\begin{array}{c}0\\ 1\\ 0\end{array}\right)\mathrm{d}\alpha \\ & ={\int }_{-1}^{1}0\mathrm{d}\alpha \\ & =0\end{array}$$