# Resources tagged with: Vector Notation and Geometry

Filter by: Content type:
Age range:
Challenge level:

### There are 20 results

Broad Topics > Vectors and Matrices > Vector Notation and Geometry ### Tetra Perp

##### Age 16 to 18 Challenge Level:

Show that the edges AD and BC of a tetrahedron ABCD are mutually perpendicular when: AB²+CD² = AC²+BD². ### A Knight's Journey

##### Age 14 to 18

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

##### Age 14 to 16 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the inner triangle? ### An Introduction to Vectors

##### Age 14 to 18

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. . . . ### Coordinated Crystals

##### Age 16 to 18 Challenge Level:

Explore the lattice and vector structure of this crystal. ### Matrix Meaning

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

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? ### Vector Walk

##### Age 14 to 18 Challenge Level:

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

##### Age 16 to 18

An account of multiplication of vectors, both scalar products and vector products. ### From Point to Point

##### Age 14 to 16 Short Challenge Level:

Can you combine vectors to get from one point to another? ##### Age 16 to 18 Challenge Level:

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? ### Polygon Walk

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Can you find the area of a parallelogram defined by two vectors? ### Vector Gem Collector

##### Age 14 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity. ### Napoleon's Theorem

##### Age 14 to 18 Challenge Level:

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? ### Spotting the Loophole

##### Age 14 to 16 Challenge Level:

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?  