Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

B = $\sqrt{7^2+{24}^2}$ = 25

and $\hat{A}$ = $\frac{\hat{A}}{A}$ = $\frac{3\hat{i}+4\hat{j}}{\sqrt{3^2+4^2}}$

= $\frac{1}{5}$ (3 $\hat{i}$ + 4 $\hat{j}$)

$\therefore$ BA = 25 $\times$ $\frac{1}{5}$ (3 $\hat{i}$ + 4 $\hat{j}$ ) = 15 $\hat{i}$ + 20 $\hat{j}$