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 solution.

Possible approach

This could form a short introduction to work on vectors.
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 three grids.
When they think they have spotted a closed loop by eye, they should verify algebraically that it is indeed a closed loop.

Key questions

What can you say about the horizontal components of the vectors in a closed loop?

Possible extension

Vector Walk begins to explore properties of vectors and combining two basic vectors to reach points on the coordinate grid.