There are **20** NRICH Mathematical resources connected to **Vector Notation and Geometry**, you may find related items under Vectors and Matrices.

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

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

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

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

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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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Use vectors to collect as many gems as you can and bring them safely home!

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

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

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

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Explore the lattice and vector structure of this crystal.

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

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

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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?

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