Vectors

There are 23 NRICH Mathematical resources connected to Vectors
Cubestick
problem

Cubestick

Age
16 to 18
Challenge level
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Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
Square coordinates
problem

Square coordinates

Age
11 to 14
Challenge level
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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
V-P Cycles
problem

V-P Cycles

Age
16 to 18
Challenge level
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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?
Air Routes
problem

Air Routes

Age
16 to 18
Challenge level
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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.
Flexi Quad Tan
problem

Flexi Quad Tan

Age
16 to 18
Challenge level
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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.
8 Methods for Three By One
problem

8 Methods for Three By One

Age
14 to 18
Challenge level
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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? Which do you like best?
Flexi Quads
problem

Flexi Quads

Age
16 to 18
Challenge level
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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?
An introduction to vectors
article

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.