Introduction:
In this problem, we are given two vectors A and B. We have to find a vector that has the same magnitude as B and is parallel to A.

Solution:
To solve this problem, we will use the concept of unit vectors. A unit vector is a vector that has a magnitude of 1. We can use unit vectors to find a vector that has the same direction as A but has a different magnitude.

Step 1: Find the unit vector of A
To find the unit vector of A, we first need to find the magnitude of A. We can use the Pythagorean theorem to find the magnitude of A:

|A| = √(3^2 + 4^2) = 5

Now we can find the unit vector of A by dividing A by its magnitude:

 = A/|A| = (3/5)î + (4/5)j

Step 2: Find the magnitude of B
To find a vector with the same magnitude as B, we first need to find the magnitude of B:

|B| = √(7^2 + 24^2) = 25

Step 3: Find the vector with the same direction as A and magnitude of B
Now we can find a vector with the same direction as A and a magnitude of B by multiplying the unit vector of A by the magnitude of B:

B' = |B|Â = 25((3/5)î + (4/5)j)

Simplifying:

B' = 15î + 20j

Therefore, the vector with the same magnitude as B and parallel to A is 15î + 20j.

Conclusion:
We have found the vector that has the same magnitude as B and is parallel to A. We used the concept of unit vectors to find a vector with the same direction as A but with a different magnitude.