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====== Vector Representations ======

===== Prompt =====

** "Write down a representation of a 2D vector." **

===== Context =====

This [[strategy:smallwhiteboard:|SWBQ]] is intended to refresh students' memories of the varying representations of vectors seen throughout undergraduate math and physics courses. Further, this SWBQ segues well into an introductory discussion of Bra-Ket notation.  

===== Wrap Up =====
Make sure that both the component representation 
$$ \vec{v} = x\hat{x} + y\hat{y}$$
and the column (or row) representation
$$\vec{v} = \begin{pmatrix} x\\y \end{pmatrix}$$
are mentioned if no students offer them as a response.\\\\
%%FIXME: might not want this info here

This can be a great opportunity to introduce the ``representation'' operator $\dot{=}$ to indicate that two equated vectors are not equal, but that one is a representation of the other in a different basis.  Students can then be introduced to equations such as
$$\vec{v} \,\dot{=} \begin{pmatrix} v_x\\v_y \end{pmatrix}\, ,$$
which implies that the vector $\vec{v}$ components $v_x$ and $v_y$ in the $x$ and $y$ basis, respectively.

{{swbq>prswvectorreps.ppt|Powerpoint slide}}
\\\\
{{swbq>prswvectprreps.pdf|PDF slide}}

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