Question

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

Answer 1

Projection of $\overrightarrow{a}=2\hat{i}+\hat{j}$ on vector $(\hat{i}+2\hat{j})$

projection = $\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}{|}^2}\overrightarrow{b}$

$=\frac{2+2}{\left(\sqrt{5}\right)}(\hat{i}+2\hat{j})$

$=\frac{4}{5}(\hat{i}+2\hat{j})$

$\frac{4\hat{i}}{5}+\frac{8\hat{i}}{5}$