Vector notation and geometry

There are 18 NRICH Mathematical resources connected to Vector notation and geometry
Areas of parallelograms
problem

Areas of parallelograms

Age
14 to 16
Challenge level
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Can you find the area of a parallelogram defined by two vectors?
Triangle in a Triangle
problem

Triangle in a Triangle

Age
14 to 16
Challenge level
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Can you work out the fraction of the original triangle that is covered by the inner triangle?
Tetra Perp
problem

Tetra Perp

Age
16 to 18
Challenge level
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Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.
Napoleon's Theorem
problem

Napoleon's Theorem

Age
14 to 18
Challenge level
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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?
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.
A Knight's Journey
article

A Knight's Journey

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