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

Answer 1

Answer: (D)

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