Dot product is proportional to cosine of angle between vectors
==============================================================

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:`vector law
<Dot product is proportional to cosine of angle between vectors (vector)>`.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.geometry.dot_product_is_proportional_to_cosine_between_vectors

.. py:data:: dot_product

    Dot product between :math:`\vec u` and :math:`\vec v`.

Symbol:
    :code:`dot(u, v)`

Latex:
    :math:`\left( \vec u, \vec v \right)`

Dimension:
    :code:`any_dimension`


.. py:data:: first_vector_length

    Length of :math:`\vec u`.

Symbol:
    :code:`u`

Latex:
    :math:`u`

Dimension:
    :code:`any_dimension`


.. py:data:: second_vector_length

    Length of :math:`\vec v`.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`any_dimension`


.. py:data:: angle_between_vectors

    :attr:`~symplyphysics.symbols.basic.angle` between :math:`\vec u` and :math:`\vec v`.

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: law

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


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