If $\overrightarrow{\mathrm{A}}=3\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}$ and $\overrightarrow{B}=7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}}$, the vector having the same magnitude as $\overrightarrow{\mathrm{B}}$ and parallel to $\overrightarrow{\mathrm{A}}$ is

$\left|\overrightarrow{\mathrm{B}}\right|$ = $\sqrt{7^2+{\left(24\right)}^2}= \sqrt{625} = 25$

Unit vector in the direction of A will be $\widehat{\mathrm{A}}=\frac{3\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}}{5}$

So required vector = $\text{25}\left(\frac{3\widehat{\mathrm{i}}+4\widehat{\mathrm{j}}}{5}\right)\mathrm{\hspace{0.17em}}=\mathrm{\hspace{0.17em}}15\widehat{\mathrm{i}}+20\widehat{\mathrm{j}}$