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Question
Find the projection of \[\vec{a} \text{ on } \vec{b} \text{ if } \vec{a} \cdot \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} .\]
Solution
\[\text{ We have }\]
\[ \vec{a} . \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} \]
\[\text{ The projection of } \vec{a} \text{ on } \vec{b }\text{ is }\]
\[\frac{\vec{a} . \vec{b}}{\left| \vec{b} \right|}\]
\[ = \frac{8}{\sqrt{4 + 36 + 9}}\]
\[ = \frac{8}{7}\]
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