Chapter 3 - Vectors in Physics - Problems and Conceptual Exercises - Page 78: 27

$(40m)\hat x+(-36m)\hat y$

First of all, we write the x and y components of the given vector $r_x=rco\theta$ $\implies r_x=(54m)cos(-42.0^{\circ})=40m$ and $r_y=rsin\theta$ $\implies r_y=(54m)sin(-42.0^{\circ})=-36m$ We can now express $\vec{\Delta r}$ in terms of unit vectors as $\vec{\Delta r}=(40m)\hat x+(-36m)\hat y$