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)` .

Explanation

`|vec(A)| = sqrt(3^(2) + 4^(2)) = 5`
Unit vector int 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)`