Halliday, Resnick & Walker — Vectors: Problem 72

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: $\vec{d}_1$ for $0.40\text{ m}$ southwest (that is, at $45^\circ$ from directly south and from directly west), $\vec{d}_2$ for $0.50\text{ m}$ due east, $\vec{d}_3$ for $0.60\text{ m}$ at $60^\circ$ north of east. Let the positive $x$ direction be east and the positive $y$ direction be north. What are (a) the $x$ component and (b) the $y$ component of $\vec{d}_1$? Next, what are (c) the $x$ component and (d) the $y$ component of $\vec{d}_2$? Also, what are (e) the $x$ component and (f) the $y$ component of $\vec{d}_3$? What are (g) the $x$ component, (h) the $y$ component, (i) the magnitude, and (j) the direction of the ant’s net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move?