Vector notation and geometry
problem
Triangle in a Triangle
Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
Tetra Perp
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.
problem
Napoleon's Theorem
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?
problem
Flexi Quads
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?
article
Multiplication of Vectors
An account of multiplication of vectors, both scalar products and
vector products.
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.
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.