### 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.

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### Key questions

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

And what about the vertical components?

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### Possible support

Students may find it helpful to draw the vectors on squared paper.

### Possible extension

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

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