Vectors

problem

Flexi Quad Tan

Age

16 to 18

Challenge level

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.
problem

Air Routes

Age

16 to 18

Challenge level

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.
problem

From Point to Point

Age

14 to 16

Challenge level

Can you combine vectors to get from one point to another?
problem

Coordinated Crystals

Age

16 to 18

Challenge level

Explore the lattice and vector structure of this crystal.
problem

Polygon Walk

Age

16 to 18

Challenge level

Go on a vector walk and determine which points on the walk are closest to the origin.
problem

Another Triangle in a Triangle

Age

16 to 18

Challenge level

Can you work out the fraction of the original triangle that is covered by the green triangle?
problem

Fix Me or Crush Me

Age

16 to 18

Challenge level

Can you make matrices which will fix one lucky vector and crush another to zero?
problem

Matrix Meaning

Age

16 to 18

Challenge level

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
problem

Nine Eigen

Age

16 to 18

Challenge level

Explore how matrices can fix vectors and vector directions.
problem

V-P Cycles

Age

16 to 18

Challenge level

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?