6. Given $a_{1}, a_{2}, b_{1}, b_{2}, \cdots, b_{k}$ are vectors in a plane, no two of which are parallel, satisfying $\left|a_{1}-a_{2}\right|=1$, and $\left|a_{i}-b_{j}\right| \in\{1,2,3\}(i=1,2 ; j=1,2, \cdots, k)$. Then the maximum value of $k$ is $\qquad$