The 'recipe' is given in the question. You need to know that the scalar
product of two perpendicular vectors is 0 so that, if one vector lies in a
plane and the other is normal to the plane, then their scalar product is zero.
This gives the equation of a plane through the origin in R3 as
v·n = a x + b y + c z = 0.
The diagram should help you to visualise that, if u0 is on the plane and n
is a vector normal to the plane, then the points u0 + t n and u0 - t n
are reflections of each other in the plane.
Where quaternions are equivalent to vectors we are not using boldface fonts
other than in introducing the unit vectors i, j, k along the axes
in R3. The quaternion functions and quaternion algebra give a neat and efficient way
to work with reflections in R3 and they are very useful in computer
graphics programs.