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प्रश्न
Write the value of \[\left( \vec{a} . \hat{i} \right) \hat{i} + \left( \vec{a} . \hat{j} \right) \hat{j} + \left( \vec{a} . \hat{k} \right) \hat{k} ,\] where \[\vec{a}\] is any vector.
उत्तर
\[\text{ Let } \vec{a} = a_1 \vec{i} + a_2 \vec{j} + a_3 \vec{k} \]
\[\text{ Now },\]
\[\left( \vec{a} . \vec{i} \right) \vec{i} + \left( \vec{a} . \vec{j} \right) \vec{j} + \left( \vec{a} . \vec{k} \right) \vec{k} \]
\[ = a_1 \vec{i} + a_2 \vec{j} + a_3 \vec{k} \]
\[ = \vec{a}\]
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