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Question
Write the projection of \[\hat{i} + \hat{j} + \hat{k}\] along the vector \[\hat{j}\]
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Solution
\[\text{ Projection of } \vec{a} \text{ on } \vec{b} =\frac{\vec{a} . \vec{b}}{\left| \vec{b} \right|}\]
\[\text{ Projection of } \vec{i} + \vec{j} + \vec{k} \text{ along } \vec{j} \]
\[ = \frac{\left( \vec{i} + \vec{j} + \vec{k} \right) . \vec{j}}{\left| \vec{j} \right|}\]
\[ = \frac{1}{1}\]
\[ = 1\]
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