已知 $\boldsymbol{e}_{1}, \boldsymbol{e}_{2}$ 是非零的不共线向量, $\boldsymbol{a}=k \boldsymbol{e}_{1}+\boldsymbol{e}_{2}, \boldsymbol{b}=\boldsymbol{e}_{1}+k^{2} \boldsymbol{e}_{2}$, 且 $\boldsymbol{a} / / \boldsymbol{b}$, 则 $k=$
$\because \boldsymbol{a} / / \boldsymbol{b}, \boldsymbol{a}=k \boldsymbol{e}_{1}+\boldsymbol{e}_{2}, \boldsymbol{b}=\boldsymbol{e}_{1}+k^{2} \boldsymbol{e}_{2}$,

$\therefore$ 存在实数 $\lambda$ 使得 $\boldsymbol{a}=\lambda \boldsymbol{b}$, 即 $\boldsymbol{k} \boldsymbol{e}_{1}+\boldsymbol{e}_{2}=\lambda\left(\boldsymbol{e}_{1}+k^{2} \boldsymbol{e}_{2}\right)$.

$\therefore k \boldsymbol{e}_{1}+\boldsymbol{e}_{2}=\lambda \boldsymbol{e}_{1}+\lambda k^{2} \boldsymbol{e}_{2}$.

$\therefore\left\{\begin{array}{l}k=\lambda, \\ 1=\lambda k^{2},\end{array} \quad \therefore k^{3}=1, \therefore k=1\right.$.