School of Mathematics and Statistics, The University of Sydney
 10. The projection of a vector
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The component of a vector parallel to a given vector

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By definition of the scalar product

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

is the projection of v into the direction of u as shown below. We call

v · u -|u|-= v · ^u

the component of v in the direction of u. The geometric picture is shown below.

v u h p = |v |cosh-u- = v-· u-u |u | |u|2

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Main menu Section menu   Previous section Next section button disabled Resolution of a vector into components parallel and perpendicular to a given vector