Answer
The interference produces a minimum all along path 2.
Work Step by Step
Every point on path 2 is a greater distance from $S_1$ than from $S_2$ by their separation distance.
Note that the separation distance of $S_1$ and $S_2$ is $1.5~\lambda$
Therefore, the path length difference is $1.5~\lambda$ for all points on path 2.
Since the sources are exactly in phase, the waves will be exactly out of phase at all points on path 2.
Therefore, the interference produces a minimum all along path 2.
