You read $\underline{r} = \underline{a} + \lambda\underline{b}$ as two points.
$\underline{a}$ locates a point on the line; $\underline{b}$ is the direction. Through $A$ and $B$, the direction is $\underline{b}-\underline{a}$, not either position vector. An intersection question wants the point, not $\lambda$.
Next time: Write every line as point $+\ \lambda \times$ direction.