The "perp dot product" 
for 
and 
vectors in the plane is a modification of the two-dimensional
dot product in which 
is replaced by the perpendicular
vector rotated 
to the left defined by Hill (1994). It satisfies the identities
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the angle from vector 
to vector 
.
