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) \[\frac{\vec{b}}{\left| \vec{b} \right|}\] 

Answer 1

(b) \[\frac{\left( \vec{a} \cdot \vec{b} \right) \vec{b}}{\left| \vec{b} \right|^2}\] 

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