Question

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

• A. $5\hat{i}+20\hat{j}$
• B. $15\hat{i}+10\hat{j}$
• C. $20\hat{i}+15\hat{j}$
• D. $15\hat{i}+20\hat{j}$

Answer 1

The correct option is D

$15\hat{i}+20\hat{j}$

$|B|=\sqrt{7^2+(24{)}^2}=\sqrt{625}=25$
Unit vector in the direction of A will be $\hat{A}=\frac{3\hat{i}+4\hat{j}}{5}$
So required vector $=25\left(\frac{3\hat{i}+4\hat{j}}{5}\right)=15\hat{i}+20\hat{j}$.