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 

Answer 1

(a) 1 

\[Let \vec{a} = \hat{i} + \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{j} \]

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

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

\[ = \frac{\left( \hat{i} + \hat{j} + \hat{k} \right) . \hat{j}}{\left| \hat{j} \right|}\]

\[ = \frac{0 + 1 + 0}{1}\]

\[ = 1\]

\[\]