Vector

Vector is a geometrical entity used in Computational Geometry, which has magnitude and direction. 

Computational Geometry Library in Python – Vector:

class CGLibPy_Vector(object):
    I = 0.0
    J = 0.0
    K = 0.0
    vecLen = 0.0  

    def __init__(self,_args):
        if len(_args) == 3: # Three Coefficients
            self.I = _args[0]
            self.J = _args[1]
            self.K = _args[2]
        elif len(_args) == 2: # Six Coordinates
            self.I = _args[1].X - _args[0].X
            self.J = _args[1].Y - _args[0].Y
            self.K = _args[1].Z - _args[0].Z
        self.vecLen = math.sqrt(self.I*self.I + self.J*self.J + self.K*self.K)

    def normalize(self):        
        self.I = self.I/self.vecLen
        self.J = self.J/self.vecLen
        self.K = self.K/self.vecLen

If a vector is defined by two point A and B then, vector direction is determined using coordinates of A and B. The magnitude of vector is determined by distance between in A and B.

→
u is defined as direction vector where,

u = (x2-x1)i + (y2-y1)j + (z2-z1)k

where, i, j and k are Unit Vectors along X,Y and Z axis respectively. Units Vectors are vectors whose magnitude is One (1). Any vector can be converted into Unit Vector by dividing each component of the vector by magnitude. So, if a vector is given as,

V = ai + bj +ck

Magnitude of vector = |AB| = √a² + b² + c² 

and

Unit Vector = (a/|AB|)i + (b/|AB|)j + (c/|AB|)k 

This process of converting a vector into a unit vector is known as Normalization of vector.

Properties of vectors:

1. Vectors are equal if magnitudes and directions are same
2. Two vectors are parallel if they are in same or opposite direction