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A simple vector toolkit dealing with vectors and points in the 3-dimensional space

Project Description


from __future__ import division added to fix division operator to use true division as in Python 3.0 instead of classic division.


Vectors is a simple library toolkit dealing with common vector and point logic in the 3-dimensional space.

Supports commonly used vector math functions including:

  • Vector magnitude
  • Addition with another vector or a real number.
  • Multiplication by another vector or a real number.
  • Dot product
  • Cross/scalar product
  • Angle between vectors
  • Check if two vectors are perpendicular, parallel or non-parallel

Github Repository


pip install vectors



There are multiple ways to create our vector instances using the vectors module.

We can first initialize some vectors and points calling their repsective class contructors as follows.

  from vectors import Point, Vector

  v1 = Vector(1, 2, 3) #=> Vector(1, 2, 3)
v2 = Vector(2, 4, 6) #=> Vector(2, 4, 6)

p1 = Point(1, 2, 6) #=> Point(1, 2, 3)
p2 = Point(2, 0, 2) #=> Point(2, 4, 6)

We can also create a Point instance or a Vector instance with a list using the class method from_list().

components = [1.2, 2.4, 3.8]

v = Vector.from_list(components) #=> Vector(1.2, 2.4, 3.8)

We can also create our Vectors from two Point instances using the classmethod from_points().

v = Vector.from_points(p1, p2) #=> Vector(1, -2, -4)

We can also get access to the vector array to use it with other libraries.

v1.vector #=> [1, 2, 3]


We can get the magnitude of the vector easily.

v1.magnitude() #==> 3.7416573867739413


We can add a real number to a vector or compute the vector sum of two vectors as follows.

v1.add(2) #=> Vector(3.0, 4.0, 5.0)

v1.sum(v2) #=> Vector(3.0, 6.0, 9.0)

Both methods return a Vector instance.


We can multiply a vector by a real number.

v1.multiply(4) #=> Vector(4.0, 8.0, 12.0)

The above returns a Vector instance.

Dot Product

We can find the dot product of two vectors. #=> 0.0

We can also use angle theta on the dot function. 180)

Dot product returns a real number.

Cross/Scalar Product

We can find the cross product of two vectors.

v1.cross(v2) #=> Vector(0, 0, 0)

Cross product returns a Vector instance, which is always perpendicular to the other two vectors.

Angle Theta

We can also find the angle theta between two vectors.

v1.angle(v2) #=> 0.0

Angle is a measured in degrees.

Parallel, Perpendicular, Non-Parallel

We can check if two vectors are parallel, perpendicular or non-parallel to each other.

v1.parallel(v2) #=> True
v1.perpendicular(v2) #=> False
v1.non_parallel(v2) #=> False

All of the above return either True or False.


  • Create Analytic Geometry Toolkit based on the vectors toolkit.
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