Question

If $\overrightarrow{a}=3\hat{i}+4\hat{j}$ & $\overrightarrow{b}=7\hat{i}+24\hat{j}$ then a vector having the same magnitude as $\overrightarrow{b}$ and same direction as
$\overrightarrow{a}$ is ____.

Answer 1

$\overrightarrow{a}=3\uparrow +4\hat{j}\overrightarrow{b}=7\hat{i}+24\hat{j}$

$\left|b\right|=\sqrt{{\left(24\right)}^2+{\left(7\right)}^2}=\sqrt{625}=25$ $-$ magnitude of $\overrightarrow{b}$

Unit vector in direction of $\overrightarrow{a},\hat{a}=\frac{3\uparrow +4\hat{j}}{\sqrt{3^2+4^2}}=\frac{3}{5}\uparrow +\frac{4}{5}\hat{j}$

$\therefore$ Required vector $=25\times \frac{3}{5}\uparrow +25\times \frac{4}{5}\hat{j}=15\uparrow +20\hat{j}$