Component Form of Vector

component_form(initial_point, terminal_point)

Calculates the component form for a vector by using two points

Parameters

  • initial_point (list of int or float) – List of numbers representing a point

  • terminal_point (list of int or float) – List of numbers representing a point

Raises

  • TypeError – Arguments must be 1-dimensional lists

  • TypeError – Elements of arguments must be integers or floats

  • ValueError – Both arguments must contain the same number of elements

Returns

components – List in which each element is the difference of the corresponding elements from the input points (specifically, the change from the initial point to the terminal point)

Return type

list of int or float

See also

vector_sum(), scalar_product_vector(), vector_direction(), vector_magnitude()

Notes

  • Initial point: \(A = (a_1, a_2, \cdots, a_n)\)

  • Terminal point: \(B = (b_1, b_2, \cdots, b_n)\)

  • Component form of vector: \(\overrightarrow{AB} = \langle b_1 - a_1, b_2 - a_2, \cdots, b_n - a_n \rangle\)

  • Component Form

Examples

Import component_form function from regressions library
>>> from regressions.vectors.components import component_form
Determine the component form of a vector with an initial point of [1, 2, 3] and a terminal point of [4, 5, 6]
>>> components_3d = component_form([1, 2, 3], [4, 5, 6])
>>> print(components_3d)
[3, 3, 3]
Determine the component form of a vector with an initial point of [-5, 12] and a terminal point of [3, -7]
>>> components_2d = component_form([-5, 12], [3, -7])
>>> print(components_2d)
[8, -19]