Extra: vectors in motion
Add up a robot's moves into one move, send it home with the opposite vector, and see how a river's current changes where a swimmer goes.
- France: grade 10
- Iran: grade 7
- Syria: grade 10
- Palestine: grade 11
- Ukraine: grade 9
- Russia: grade 9
Guide
A vector is a move: so far across, so far up. Moves one after another add up head to tail, and the arrow from the very start to the very end is the total move. A robot football player that goes u, then v, then w ends up where u + v + w takes it.
The way back is the opposite vector: the same length, the other way. If the total move is 25, the way home is −2−5.
A swimmer in a river moves in two ways at once: her own swimming and the water carrying her. Where she really goes is the sum of the two vectors. The current does not just make her faster: it pushes her sideways. To land straight across, she has to aim a little upstream, so that the current straightens her path.