Chapter 12 - Vectors and the Geometry of Space - 12.2 Exercises - Page 822: 3

Vector AB = Vector DC Vector DA = Vector CB Vector DE = Vector EB Vector EA = Vector CE

Equal vectors must have the same magnitude (length) and direction. Since opposite sides of a parallelogram are parallel and congruent, these vector pairs will have the same magnitude (because congruent sides have the same length) and direction (because parallel lines have the same slope): Vector AB = Vector DC Vector DA = Vector CB We also have that: Vector DE = Vector EB Vector EA = Vector CE These pairs have the same magnitude because diagonals bisect each other in a parallelogram, and by looking at the figure it’s evident that they’re pointing in the same direction.