Question

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

• A. $15\hat{i}+20\hat{j}$
• B. $5\hat{i}-3\hat{j}$
• C. $15\hat{i}+13\hat{j}$
• D. $5\hat{i}+14\hat{j}$

Answer 1

Answer: (A)

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

Unit vector in the direction of A will be

$=\frac{3\hat{i}+4\hat{j}}{\sqrt{3^2+4^2}}=\frac{3\hat{i}+4\hat{j}}{5}$

$|B|=\sqrt{7^2+(24{)}^2}$

$=\sqrt{625}=25$

Required vector $=25\left(\frac{3\hat{i}+4\hat{j}}{5}\right)=15\hat{i}+20\hat{j}$