Play countdown with vectors.
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?
Take any parallelogram and draw squares on the sides of the
parallelogram. What can you prove about the quadrilateral formed by
joining the centres of these squares?
Can you work out the fraction of the original triangle that is
covered by the inner triangle?
Find out how the quaternion function G(v) = qvq^-1 gives a simple
algebraic method for working with rotations in 3-space.
Show that the edges AD and BC of a tetrahedron ABCD are mutually
perpendicular when: AB²+CD² = AC²+BD².