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Vector Countdown

Age 16 to 18 Challenge Level:

Vectors in three dimensions can be added, subtracted and 'multiplied' using the scalar and cross products. They can also be multiplied or divided by a scalar. You can also find the modulus of a vector. Why not put your knowledge and intuition concerning vectors to the test in a game of vector countdown? You can use each vector given at most once, but you can use the results of a vector calculation in a new game; if you need a scalar then you will need to use the modulus or scalar product operations on one or two of the vectors. We recommend about 5 minutes per game. You can determine how close you get to the target by looking at the modulus of the difference between your answer and the target vector.
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Extension: If you wish to develop your IT skills, why not try implementing a version of this game on a spreadsheet or in code? As an extra challenge you might try to implement a version in which you know that there is always an exact solution for every game played.