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Question
The orthogonal projection of \[\vec{a} \text{ on } \vec{b}\] is
Options
(a) \[\frac{\left( \vec{a} \cdot \vec{b} \right) \vec{a}}{\left| \vec{a} \right|^2}\]
(b) \[\frac{\left( \vec{a} \cdot \vec{b} \right) \vec{b}}{\left| \vec{b} \right|^2}\]
(c) \[\frac{\vec{a}}{\left| \vec{a} \right|}\]
(d) \[\frac{\vec{b}}{\left| \vec{b} \right|}\]
Solution
(b) \[\frac{\left( \vec{a} \cdot \vec{b} \right) \vec{b}}{\left| \vec{b} \right|^2}\]
\[\text{ The orthogonal projection of }\vec{a} \text{ on } \vec{b} \text{ is }\]
\[\frac{\left( \vec{a} . \vec{b} \right) \vec{b}}{\left| \vec{b} \right|^2}\]
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