Unit Vector

unit_vector(vector)

Calculates the unit vector corresponding to a given vector (and therefore having the same direction)

Parameters

vector (list of int or float) – List of numbers representing a vector

Raises

  • TypeError – Argument must be a 1-dimensional list

  • TypeError – Elements of argument must be integers or floats

Returns

unit – Vector with a magnitue of 1 in the same direction as the original vector

Return type

list of float

See also

component_form(), scalar_product_vector(), vector_direction(), vector_magnitude()

Notes

  • Comparison vector: \(\mathbf{a} = \langle a_1, a_2, \cdots, a_n \rangle\)

  • Unit vector with same direction: \(\mathbf{u}= \frac{\mathbf{a}}{\|\mathbf{a}\|}\)

  • Unit Vector

Examples

Import unit_vector function from regressions library
>>> from regressions.vectors.unit import unit_vector
Determine the unit vector of the vector with components [7, 5, -1]
>>> unit_3d = unit_vector([7, 5, -1])
>>> print(unit_3d)
[0.8082903768654759, 0.5773502691896257, -0.11547005383792514]
Determine the unit vector of the vector with components [3, 2]
>>> unit_2d = unit_vector([3, 2])
>>> print(unit_2d)
[0.8320502943378437, 0.5547001962252291]