Points, Euclidean vectors

A point (i.e. an element of R²) is represented by a list (x y). An n-dimensional Euclidean vector is represented by a list with n elements. The following function are provided to manipulate points and vectors:

(zero-vector? v)    // true iff v = 0
(equal-vectors p q)
(equal-points p q)
(norm l)            // euclidean norm of vector l
(distance p q)      // euclidean distance between p and q

(unit-vector v)     // v/|v|
(vect-less v1 v2)   //  v1 - v2
(vect-plus v1 v2)   // v1 + v2
(vect-times a v)    // a*v

(rth->xy r th)      // returns (x,y) associated with polar coordinates (r,th)
(point-angle-2pi p) // angle in [0,2pi) associated with the point p
(point-angle+pi-pi p) // angle in [-pi,pi) associated with the point p

(get-point P1 P2 d) // returns  a point d units apart from P2 
                    // in the direction of the vector P1P2