If vec(A) = 3 hat(i) + 4 hat(j) and vec(B) = 7 hat(i) + 24 hat(j) , then find a vector having the same magnitudes as vec(B)and parallel to vec(A) .

If vec(A) = 3 hat(i) + 4 hat(j) and vec(B) = 7 hat(i) + 24 hat(j) , th

1.	If vec(A) = 3 hat(i) + 4 hat(j) and vec(B) = 7 hat(i) + 24 hat(j) , then find a vector having the same magnitudes as vec(B)and parallel to vec(A) .
Answer» Solution :`\|vec(A)\| = sqrt(3^(2) + 4^(2)) = 5` Unit vectorint he direction of `vec(A)`is `HAT(A) = (vec(A))/(\|vec(A)\|)= (1)/(5) (3 hat(i) + 4 hat(J))` Also`\|vec(B)\| = sqty(7^(2) + 24^(2)) = 25` The vector having the same magnitude as `vec(B)` and parallel to `vec(A)` . `= \|vec(B)\| hat(A) = 25 XX (1)/(5) (3 hat(i) + 4 hat(j))` `= 5 ( 3 hat(i) + 4 hat(j)) = 15 hat(i) + 20 hat(j)`