question_answer

Find the projection of vector \[2\hat{i}+\hat{j}\] on the vector \[\hat{i}+2\hat{j}.\]

Answer:

Let \[\overrightarrow{a}=2\,\hat{i}+\hat{j}\]and \[\overrightarrow{b}=\hat{i}+2\hat{j}\] Projection of vector \[\overrightarrow{a}\]and \[\overrightarrow{b}\] \[=\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{|\overrightarrow{b}|}=\frac{(2\,\hat{i}+\hat{j})\cdot (\hat{i}+2\hat{j})}{\sqrt{{{(1)}^{2}}+{{(2)}^{2}}}}=\frac{2+2}{\sqrt{5}}=\frac{4}{\sqrt{5}}\]