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There are **20** NRICH Mathematical resources connected to **Vector notation and geometry**, you may find related items under Vectors and matrices.

Game
Primary curriculum
Secondary curriculum
### Vector Gem Collector

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Vector Journeys

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?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Vector Walk

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spotting the Loophole

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Areas of Parallelograms

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle in a Triangle

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

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Multiplication of Vectors

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

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### An Introduction to Vectors

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 why they are useful.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Tetra Perp

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flexi Quads

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### From Point to Point

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

Age 14 to 16

ShortChallenge Level

Problem
Live Primary curriculum
Secondary curriculum
### Matrix Meaning

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Walk

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinated Crystals

Explore the lattice and vector structure of this crystal.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hold Still Please

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quaternions and Rotations

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spiroflowers

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Napoleon's Theorem

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?

Age 14 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### A Knight's Journey

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

Age 14 to 18