### There are 20 results

Broad Topics >

Vectors and Matrices > Vector Notation and Geometry

##### 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.

##### 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.

##### 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?

##### 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?

##### 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. . . .

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

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

##### Age 16 to 18

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

##### Age 11 to 16 Challenge Level:

The classic vector racing game.

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

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

##### 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?

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

Explore the lattice and vector structure of this crystal.

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

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

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

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

##### 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.

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

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

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

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

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

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

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

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

##### 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?

##### 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.