In this maths problem from NRICH, students are encouraged to think geometrically about vectors in order to deduce which vectors could generate particular sets of points.
When students have a feel for how two vectors can be used to reach a variety of points on the plane, they can be asked to sketch possible arrangements of points around the origin forming an equilateral triangle, and a hexagon, using points which can be reached using the vector i. Some calculation will be needed to work out the second vector needed to reach the appropriate points.
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