تصویر (بردار)

${\displaystyle \left\vert \operatorname {proj} _{\vec {b}}{\vec {a}}\right\vert ={\vec {a}}\cdot {\hat {b}}=\left\vert {\vec {a}}\right\vert \cos {\theta }}$[2]

${\displaystyle \operatorname {proj} _{\vec {b}}{\vec {a}}=({\vec {a}}\cdot {\hat {b}})\ {\hat {b}}=(\left\vert {\vec {a}}\right\vert \cos {\theta })\ {\hat {b}}}$

${\displaystyle \operatorname {proj} _{\vec {b}}{\vec {a}}=({\vec {a}}\cdot {\hat {b}})\ {\hat {b}}={{\vec {a}}\cdot {\vec {b}} \over \left\vert {\vec {b}}\right\vert ^{2}}{\vec {b}}}$[2]

که در آن ${\displaystyle {\hat {b}}}$ برابر بردار یکّهٔ ${\displaystyle {\vec {b}}}$ است.

توجّه داشته باشید که ${\displaystyle \cos {\theta }}$ را می‌توان از رابطهٔ ${\displaystyle \cos {\theta }={{\vec {a}}\cdot {\vec {b}} \over \left\vert {\vec {a}}\right\vert \left\vert {\vec {b}}\right\vert }}$ محاسبه کرد[2].

1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-09-07.
2. «۱۲٫۳». Thomas' Calculus (14th Edition).