Vectors

problem

Air Routes

Age

16 to 18

Challenge level

2 out of 3

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

3 out of 3

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

Flexi Quad Tan

Age

16 to 18

Challenge level

1 out of 3

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

Coordinated Crystals

Age

16 to 18

Challenge level

1 out of 3

Explore the lattice and vector structure of this crystal.
problem

Polygon Walk

Age

16 to 18

Challenge level

1 out of 3

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

2 out of 3

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

2 out of 3

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

Matrix Meaning

Age

16 to 18

Challenge level

2 out of 3

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

Nine Eigen

Age

16 to 18

Challenge level

2 out of 3

Explore how matrices can fix vectors and vector directions.
problem

V-P Cycles

Age

16 to 18

Challenge level

3 out of 3

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?