.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "matplotlib/plot_proj.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_matplotlib_plot_proj.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_matplotlib_plot_proj.py:


Projection and rejection of a vector (2D)
==============================================

For a given :math:`\vec{a}` and :math:`\vec{b}`,

.. math::
  \vec{c} = \frac{\langle \vec{a}, \vec{b}\rangle}{\langle \vec{a}, \vec{a}\rangle }\vec{a},
  \qquad
  \vec{n} = \vec{b} - \vec{c},
  \qquad
  \text{where } \langle \cdot, \cdot\rangle \text{ is a inner product.}

.. GENERATED FROM PYTHON SOURCE LINES 14-48



.. image-sg:: /matplotlib/images/sphx_glr_plot_proj_001.png
   :alt: plot proj
   :srcset: /matplotlib/images/sphx_glr_plot_proj_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt

    fig, ax = plt.subplots(1,1, figsize=(6,6))


    a = np.array([5,2])
    b = np.array([1,4])
    ba = b -a
    c = np.dot(a,b)/np.dot(a,a) * a
    n = b - c

    tdx = 0.2
    plt.quiver(0,0, a[0],a[1], color='k',angles='xy', scale_units='xy', scale=1)#, label=r"$\mathbf{a}$")
    ax.text(a[0]/2, a[1]/2-tdx, r"$\vec{a}$")

    plt.quiver(0,0, b[0], b[1], color='k',angles='xy', scale_units='xy', scale=1)
    ax.text(b[0]/2 - tdx, b[1]/2, r"$\vec{b}$")

    plt.quiver(a[0],a[1], ba[0],ba[1], color='k',angles='xy', scale_units='xy', scale=1)
    ax.text((b[0]+a[0])/2 + tdx , (b[1]+a[1])/2 + tdx, r"$\vec{b} - \vec{c}$")


    plt.quiver(0,0, c[0], c[1], color="c",angles='xy', scale_units='xy', scale=1)
    ax.text(c[0]/2, c[1]/2 -tdx, r"$\vec{c}$")

    plt.quiver(c[0], c[1], n[0], n[1], color="m",angles='xy', scale_units='xy', scale=1)
    ax.text((c[0] - n[0])/2 + tdx, (c[1] + n[1])/2, r"$\vec{n}$")


    ax.set_xlim(0,5)
    ax.set_ylim(0,5)
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.170 seconds)


.. _sphx_glr_download_matplotlib_plot_proj.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_proj.py <plot_proj.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_proj.ipynb <plot_proj.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_