The Inner Product

* Fire Engine problem

* Distance, length, norm, inner product

** From inner product to norm

** Properties of inner product of vectors over R

** Norm is geometric length of arrow

* Orthogonality

** Properties of orthogonality

** Orthogonality helps solve the fire engine problem

* Decomposition of b into parallel and perpendicular components

** Closest-Point Corollary

** Computing the projections

** Projecting along “nearly zero” vectors

* Solution to the fire engine problem

* Best approximation

** Towards solving the higher-dimensional version of best approximation

* 
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