$$ \begin{array}{rclrr} \vec{a}_1 &=& (a,& 0,& 0)\\ \vec{a}_2 &=& (b_1,& b_2,& 0)\\ \vec{a}_3 &=& (c_1,& c_2,& c_3) \end{array} $$

$$ \left| {\vec a} \right| \ne \left| {\vec b} \right| \ne \left| {\vec c} \right| $$