Tpical backyard ants often create a network of chemical trails for guidance. Extending out ward from the nest, a trail branches (bifurcates) repeatedly, with 60^(@) between the branches. If a roaming an chances upon a trail, it can tell the way to the nest at any branch point: If it is moving away from the nest, it has two choice of path requiring a small turn in its travel direction, either 30^(@) leftward or 30^(@) rightward. If it is moving toward the nest, it has only one such choice. shows a typical ant trail, with lettered straight sections of 2.0cm length and symmetric bifurcation of 60^(@). Path v is parallel to the y axis. What are the (a) magnitude and (b) angle (relative to the positive direction of the superimposed x axis) of an ant's displacement from the nest (find it in the figure) if the ant enters the trail at point A ? What are the (c ) magnitude and (d) angle if it enters at point B ?