School of Mathematics and Statistics, The University of Sydney
 10. The projection of a vector
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Resolution of a vector into components parallel and perpendicular to a given vector

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Given two vectors u and v we want to find the projections of v parallel and perpendicular to the vector v. We already know that the projection of v into the direction of u is

             u    v · u p =  |v |cosh--- = ----2 u = (v · ^u)^u             |u|    |u|

Looking at the picture below it is evident that the projection of v into the direction perpendicular to u is n = v - p, that is,

                -u-        v ·-u n = v - |v |cosh|u| = v -  |u|2 u = v -  (v ·u^)^u

          - p                 v  n=v-p                                  u                       p =  u-· v-u                          |u|2

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