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?
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?
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.
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.
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?
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?
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.