game
Favourite
Vector gem collector
Use vectors to collect as many gems as you can and bring them safely home!
Vector notation and geometry
problem
Favourite
Tetra perp
Age
16 to 18
Challenge level
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
Favourite
Triangle in a triangle
Age
14 to 16
Challenge level
Can you work out the fraction of the original triangle that is covered by the inner triangle?
problem
Favourite
Areas of parallelograms
Age
14 to 16
Challenge level
Can you find the area of a parallelogram defined by two vectors?
problem
Favourite
Spotting the loophole
Age
14 to 16
Challenge level
A visualisation problem in which you search for vectors which sum
to zero from a jumble of arrows. Will your eyes be quicker than
algebra?
problem
Favourite
Vector walk
Age
14 to 18
Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Favourite
Vector journeys
Age
14 to 18
Challenge level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem
Favourite
Flexi quads
Age
16 to 18
Challenge level
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?
problem
From point to point
Age
14 to 16
Challenge level
Can you combine vectors to get from one point to another?