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Broad Topics > Vectors > Vector Notation and Geometry

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Vector Racer

Stage: 3 and 4 Challenge Level: Challenge Level:1

The classic vector racing game.

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Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

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Vector Walk

Stage: 4 and 5 Challenge Level: Challenge Level:1

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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Spotting the Loophole

Stage: 4 Challenge Level: Challenge Level:1

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

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Areas of Parallelograms

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find the area of a parallelogram defined by two vectors?

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Multiplication of Vectors

Stage: 5

An account of multiplication of vectors, both scalar products and vector products.

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An Introduction to Vectors

Stage: 4 and 5

The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .

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Tetra Perp

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Show that the edges AD and BC of a tetrahedron ABCD are mutually perpendicular when: AB²+CD² = AC²+BD².

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Flexi Quads

Stage: 5 Challenge Level: Challenge Level:1

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

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From Point to Point

Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you combine vectors to get from one point to another?

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Vector Countdown

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Play countdown with vectors.

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Matrix Meaning

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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Polygon Walk

Stage: 5 Challenge Level: Challenge Level:1

Go on a vector walk and determine which points on the walk are closest to the origin.

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Coordinated Crystals

Stage: 5 Challenge Level: Challenge Level:1

Explore the lattice and vector structure of this crystal.

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Hold Still Please

Stage: 5 Challenge Level: Challenge Level:1

Can you arrange a set of charged particles so that none of them start to move when released from rest?

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Quaternions and Rotations

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

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Spiroflowers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

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Triangle in a Triangle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you work out the fraction of the original triangle that is covered by the inner triangle?

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Napoleon's Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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Thebault's Theorem

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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An Introduction to Complex Numbers

Stage: 5

A short introduction to complex numbers written primarily for students aged 14 to 19.

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A Knight's Journey

Stage: 4 and 5

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.