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'Spotting the Loophole' printed from http://nrich.maths.org/
Why do this problem?
This problem encourages students to use visualisation to help
them to spot a solution which can then be verified using algebra.
It shows students the power of using visual representations to
solve vector problems, often the quickest route to a
This could form a short introduction to work on
Display the example grids on the board, showing the three vectors
forming a closed loop and the four vectors on the right which do
not have a zero sum.
Then challenge students to find any closed loops in each of the
When they think they have spotted a closed loop by eye, they should
verify algebraically that it is indeed a closed loop.
What can you say about the horizontal components of the
vectors in a closed loop?
And what about the vertical components?
begins to explore properties of vectors and combining two
basic vectors to reach points on the coordinate grid.
Students may find it helpful to draw the vectors on squared