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

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

Tardigrade Admin · Accepted Answer

|B|=√72+(24)2=√625=25 Unit vector in the direction of A will be A =(3 hat i +4 hat j /5) So required vector =25((3 hat i +4 hat j /5))=15 hat i +20 hat j

Q. 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

$5 \hat{i} + 20 \hat{j}$

$15 \hat{i} + 10 \hat{j}$

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

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

$< b r / > ∣ B ∣ = 7^{2} + (24)^{2} = 625 = 25 < b r / >$
Unit vector in the direction of $A$ will be $A = \frac{3 i ^ + 4 j ^}{5}$
So required vector $= 25 (\frac{3 i ^ + 4 j ^}{5}) = 15 \hat{i} + 20 \hat{j}$

Q. If A=3i^+4j^​ and B=7i^+24j^​ , then the vector having the same magnitude as B and parallel to A is

5i^+20j^​

15i^+10j^​

20i^+15j^​

15i^+20j^​