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'Vector Walk' printed from http://nrich.maths.org/
Try creating some walks from combinations of $b_1$ and $b_2$. Do
you notice anything about the destinations you reach? Can you
explain what you find?
What is the simplest horizontal step you can make by combining
$b_1$ and $b_2$ steps? What about vertically?
This problem builds on GCSE level
vector work, and provides a foundation for concepts met in the
later Core A Level modules.