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Resources tagged with Vectors similar to Quaternions and Reflections:

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Broad Topics > Vectors > Vectors

Stage: 5 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?

From Point to Point

Stage: 4 Short Challenge Level:

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

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. . . .

Multiplication of Vectors

Stage: 5

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

Vector Journeys

Stage: 4 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 Racer

Stage: 3 and 4 Challenge Level:

The classic vector racing game.

V-P Cycles

Stage: 5 Challenge Level:

Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?

Stage: 5 Challenge Level:

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

Cubestick

Stage: 5 Challenge Level:

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Spotting the Loophole

Stage: 4 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?

Vector Countdown

Stage: 5 Challenge Level:

Play countdown with vectors.

Matrix Meaning

Stage: 5 Challenge Level:

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

Polygon Walk

Stage: 5 Challenge Level:

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

Another Triangle in a Triangle

Stage: 5 Challenge Level:

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

Coordinated Crystals

Stage: 5 Challenge Level:

Explore the lattice and vector structure of this crystal.

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.

Air Routes

Stage: 5 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Vector Walk

Stage: 4 and 5 Challenge Level:

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

Areas of Parallelograms

Stage: 4 Challenge Level:

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

8 Methods for Three by One

Stage: 4 and 5 Challenge Level:

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .

Fix Me or Crush Me

Stage: 5 Challenge Level:

Can you make matrices which will fix one lucky vector and crush another to zero?

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.

Which Twin Is Older?

Stage: 5

A simplified account of special relativity and the twins paradox.

The Use of Mathematics in Computer Games

Stage: 5

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.