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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