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STEM - living world. Biology. Exponential and Logarithmic Functions. Maths Supporting SET. Physics. Investigations. Mathematical modelling. Chemistry. Vectors. Iteration.There are 24 results
Broad Topics > Vectors and Matrices > Vectors
Fix Me or Crush Me
Age 16 to 18 Challenge Level:
Can you make matrices which will fix one lucky vector and crush another to zero?
Matrix Meaning
Age 16 to 18 Challenge Level:
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Coordinated Crystals
Age 16 to 18 Challenge Level:
Explore the lattice and vector structure of this crystal.
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.
Vector Walk
Age 14 to 18 Challenge Level:
Starting with two basic vector steps, which destinations can you reach on a vector walk?
The Use of Mathematics in Computer Games
Age 16 to 18
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
Air Routes
Age 16 to 18 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.
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. . . .
Vector Gem Collector
Age 14 to 18 Challenge Level:
Use vectors to collect as many gems as you can and bring them safely home!
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?
Multiplication of Vectors
Age 16 to 18
An account of multiplication of vectors, both scalar products and vector products.
V-P Cycles
Age 16 to 18 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?
Flexi Quads
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?
8 Methods for Three by One
Age 14 to 18 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?. . . .
Flexi Quad Tan
Age 16 to 18 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
Age 16 to 18 Challenge Level:
Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
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.
Another Triangle in a Triangle
Age 16 to 18 Challenge Level:
Can you work out the fraction of the original triangle that is covered by the green triangle?
Areas of Parallelograms
Age 14 to 16 Challenge Level:
Can you find the area of a parallelogram defined by two vectors?
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?
From Point to Point
Age 14 to 16 Short Challenge Level:
Can you combine vectors to get from one point to another?
NRICH is part of the family of activities in the Millennium Mathematics Project.