Question

Find the projection of \[\vec{a} \text{ on } \vec{b} \text{ if } \vec{a} \cdot \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} .\] 

Answer 1

\[\text{ We have }\]

\[ \vec{a} . \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} \]

\[\text{ The projection of } \vec{a} \text{ on } \vec{b  }\text{  is }\]

\[\frac{\vec{a} . \vec{b}}{\left| \vec{b} \right|}\]

\[ = \frac{8}{\sqrt{4 + 36 + 9}}\]

\[ = \frac{8}{7}\]