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Question
The projection of the vector \[\hat{i} + \hat{j} + \hat{k}\] along the vector of \[\hat{j}\] is
Options
(a) 1
(b) 0
(c) 2
(d) −1
(e) −2
Solution
(a) 1
\[Let \vec{a} = \hat{i} + \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{j} \]
\[\text{ The projection of } \vec{a} \text{ on } \vec{b} \text{ is }\]
\[\frac{\vec{a} . \vec{b}}{\left| \vec{b} \right|}\]
\[ = \frac{\left( \hat{i} + \hat{j} + \hat{k} \right) . \hat{j}}{\left| \hat{j} \right|}\]
\[ = \frac{0 + 1 + 0}{1}\]
\[ = 1\]
\[\]
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