If $\overrightarrow{b}=3\hat{i}+4\hat{j}\text{and}\overrightarrow{a}=\hat{i}-\hat{j}$ the vector having the same magnitude as that of $\overrightarrow{b}$ and parallel to $\overrightarrow{a}$ is

$\overline{a}=\hat{i}-\hat{j}$

$\left|\overrightarrow{b}\right|=5$

Unit vector along $\overline{a}$  

$\overrightarrow{a}=\hat{a}=\frac{\overrightarrow{a}}{\left|\overline{a}\right|}$

$\hat{a}=\frac{\hat{i}-\hat{j}}{\sqrt{2}}$

Now a vector of magnitude equal to $\overline{b}$ is parallel to $\overline{a}$  is

$\overline{c}=\left|\overline{b}\right|.\hat{a}$

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