What are some "interesting" and creative problems or exercises on specifically 2-dimensional vector geometry that a high school student might find compelling to solve?
The class' current knowledge consists of basic vector arithmetic, parametric vector equations of lines, the scalar dot product and pretty much everything that can be done with it algebraically and geometrically. No matrices are known at this stage.
I can think of many "mathematically glamorous" problems in 3D vector geometry, but not in 2D. It seems to me that any 2D vector problem (at high school level) instantly reduces to either some standard application of the scalar product or instantly translates into a linear system of equations, and that there is little room to pose something with more depth. Any ideas would be appreciated.