This readme file provides an overview and usage instructions for the Vector class and its operations defined in the provided Python code.
The Vector class represents a vector in n-dimensional space. It supports various vector operations, including addition, subtraction, scalar multiplication, dot product, cross product, angle calculations, and more.
This code was authored by Siddhartha Purwar.
The Vector class is designed to work with n-dimensional vectors represented as lists or tuples of int, float, or Decimal values. The class provides the following key methods:
__add__(self, v: object): Adds two vectors.__sub__(self, v: object): Subtracts one vector from another.__mul__(self, v: object): Multiplies the vector by a scalar or calculates the dot product with another vector.__truediv__(self, v: object): Divides the vector by a scalar or another vector.get_unit_vector(self): Returns the unit vector of the current vector.get_angle_with(self, v: object, in_degrees=False): Calculates the angle between two vectors.is_orthogonal_to(self, v: object): Checks if the vector is orthogonal to another vector.is_parallel_to(self, v: object): Checks if the vector is parallel to another vector.get_parallel_to(self, v: object): Returns the component of the vector parallel to another vector.get_orthogonal_to(self, v: object): Returns the component of the vector orthogonal to another vector.get_cross_product(self, v: object): Calculates the cross product of two vectors.get_parallelogram_area_with(self, v: object): Calculates the area of the parallelogram formed by two vectors.get_triangle_area_with(self, v: object): Calculates the area of the triangle formed by two vectors.
The Vector class is useful for performing various vector operations in mathematical calculations, physics simulations, computer graphics, and machine learning applications.
Below is an example of how to use the Vector class:
# Create two Vector objects v1 and v2
v1 = Vector([0, 0, 1])
v2 = Vector([1, 2, 9])
# Perform vector addition, subtraction, scalar multiplication, and dot product
v1_plus_v2 = v1 + v2
v1_minus_v2 = v1 - v2
v1_times_10 = v1 * 10
dot_product_v1_v2 = v1 * v2
# Print the results of the operations
print(f"v1 + v2 is equal to {v1_plus_v2}")
print(f"v1 - v2 is equal to {v1_minus_v2}")
print(f"v1 * 10 is equal to {v1_times_10}")
print(f"Dot product of v1 and v2 is equal to {dot_product_v1_v2}")
# Calculate the magnitude of v1 and print the result
magnitude_v1 = v1.magnitude
print(f"The magnitude of v1 is {magnitude_v1}")
# Calculate the unit vector of v1 and print the result
unit_vector_v1 = v1.get_unit_vector()
print(f"The unit vector of v1 is {unit_vector_v1}")
# Calculate the angle between v1 and v2 (in radians) and print the result
angle_v1_v2_radians = v1.get_angle_with(v2, in_degrees=False)
print(f"Angle between v1 and v2 (in radians) is equal to {angle_v1_v2_radians}")
# Check if v1 is orthogonal and parallel to v2 and print the results
is_orthogonal_v1_v2 = v1.is_orthogonal_to(v2)
is_parallel_v1_v2 = v1.is_parallel_to(v2)
print(f"Is v1 orthogonal to v2? {is_orthogonal_v1_v2}")
print(f"Is v1 parallel to v2? {is_parallel_v1_v2}")
# Calculate the component of v1 parallel and orthogonal to v2 and print the results
v1_parallel_to_v2 = v1.get_parallel_to(v2)
v1_orthogonal_to_v2 = v1.get_orthogonal_to(v2)
print(f"V1's component parallel to v2 is {v1_parallel_to_v2}")
print(f"V1's component orthogonal to v2 is {v1_orthogonal_to_v2}")
# Check if v1 can be represented as the sum of its components parallel and orthogonal to v2 and print the result
is_v1_parallel_orthogonal_to_v2 = v1 == v1_parallel_to_v2 + v1_orthogonal_to_v2
print(
f"V1 = V1's component parallel to v2 + V1's component orthogonal to v2? {is_v1_parallel_orthogonal_to_v2}"
)
# Calculate the angle between v2 and its component parallel to v1 (in degrees) and print the result
angle_v2_with_parallel_to_v1 = v2.get_angle_with(
v1.get_parallel_to(v2), in_degrees=True
)
print(
f"Angle between v2 and its component parallel to v1 (in degrees) is {angle_v2_with_parallel_to_v1}"
)
# Calculate the angle between v2 and its component orthogonal to v1 (in degrees) and print the result
angle_v2_with_orthogonal_to_v1 = v2.get_angle_with(
v1.get_orthogonal_to(v2), in_degrees=True
)
print(
f"Angle between v2 and its component orthogonal to v1 (in degrees) is {angle_v2_with_orthogonal_to_v1}"
)
# Calculate the cross product of v1 and v2 and print the result
cross_v1_v2 = v1.get_cross_product(v2)
print(f"v1 x v2 is equal to: {cross_v1_v2}")
# Calculate the area of the parallelogram formed by v1 and v2 and print the result
parallelogram_area = v1.get_parallelogram_area_with(v2)
print(f"Parallelogram area between v1 and v2 is: {parallelogram_area}")
# Calculate the area of the triangle formed by v1 and v2 and print the result
triangle_area = v1.get_triangle_area_with(v2)
print(f"Triangle area between v1 and v2 is: {triangle_area}")