Dot product is proportional to cosine of angle between vectors (vector)
=======================================================================

The dot product of two vectors is a scalar binary operation that can be defined as the product of
the norms of the vectors and the cosine of the angle between them. Also see the :ref:`scalar law
<Dot product is proportional to cosine of angle between vectors>`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Dot_product#Geometric_definition>`__.

.. py:currentmodule:: symplyphysics.mathematics.geometry.dot_product_is_proportional_to_cosine_between_vectors

.. py:data:: first_vector

    First vector.

Symbol:
    :code:`u`

Latex:
    :math:`{\vec u}`

Dimension:
    :code:`any_dimension`


.. py:data:: second_vector

    Second vector.

Symbol:
    :code:`v`

Latex:
    :math:`{\vec v}`

Dimension:
    :code:`any_dimension`


.. py:data:: angle_between_vectors

    :attr:`~symplyphysics.symbols.basic.angle` between :attr:`~first_vector` and :attr:`~second_vector`.

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`dot(u, v) = norm(u) * norm(v) * cos(phi)`


    Latex:
        .. math::
            \left( {\vec u}, {\vec v} \right) = \left \Vert {\vec u} \right \Vert \left \Vert {\vec v} \right \Vert \cos{\left(\varphi \right)}