Final answer:
Ariane's resultant displacement vector points to the southwest direction.
Step-by-step explanation:
To find the direction of Ariane's resultant displacement vector, we can use the concept of vector addition. Ariane initially drives south for 7.0 km and then turns west and drives west for 1.4 km.
If we represent south as the negative y-direction and west as the negative x-direction, we can add these displacements vectorially. The vector representing the 7.0 km south displacement would be (0, -7.0) and the vector representing the 1.4 km west displacement would be (-1.4, 0). Adding these vectors gives us a resultant displacement vector of (-1.4, -7.0).
Therefore, Ariane's resultant displacement vector points to the southwest direction.