See how 4 dimensional quaternions involve vectors in 3-space and
how the quaternion function F(v) = nvn gives a simple algebraic
method of working with reflections in planes in 3-space.
Stage: 5 Challenge Level:
Let $P_1$ be a plane through the points $A(2,1,0), B(1,1,1)$ and
$C(1,7,3)$ and $P_2$ be a plane through the points $A$, $B$ and
$V(x,y,z)$. Find all the points $V(x,y,z)$ such that the two planes
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.