Introduction to vector.project

vector.project is a function that projects a vector onto another vector. When the projection of a vector goes to infinity, vector.project returns infinity.

Usage

The function takes two vectors as arguments, and returns a new vector. Here's an example:

import numpy as np

v1 = np.array([1,2,3])
v2 = np.array([4,5,6])

# Given that the projection of v1 onto v2 goes to infinity,
# vector.project returns infinity
proj_v = np.dot(v1, v2) / np.dot(v2, v2) * v2

if np.isinf(proj_v).all():
    print("The projection of v1 onto v2 goes to infinity")
else:
    print("The projection of v1 onto v2 is: ", proj_v)

Explanation

Vectors can be thought of as arrows with a certain length and direction. When one vector is projected onto another, the resulting vector represents the component of the first vector that lies in the direction of the second vector.

The formula for projecting a vector v onto a vector w is: proj_v_w = (v . w) / (w . w) * w, where . denotes the dot product. When the dot product of v and w is equal to zero, the vectors are perpendicular and the projection is the zero vector. When the dot product of v and w is negative, the projection points in the opposite direction of w.

When the dot product of v and w is positive, the projection points in the same direction as w. If the magnitude of v is smaller than the magnitude of w, the projection will be shorter than v. However, if the magnitude of v is larger than the magnitude of w, the projection will be longer than v.

If the dot product of v and w is infinite, the projection of v onto w goes to infinity, and vector.project returns infinity. This happens when the angle between v and w is zero, i.e., when v and w are parallel and point in the same direction.