If `vec A =3 hat I + 4 hat j ` and `vec B =7hat I + 14 hat j`, find a vector having the some magnitude as `vec A` and parallel to `vec B`.

Explanation

Here,` | vec A| =sxqart 3^(2) + 4^(2) =5` ,
`|vec B| =sqrt 7^(2) + 24 ^(2) =25`
Unit vector in the direction of `vec B` is
`hat B =(vec B)/B = (7 hat I + 24 hat j)/(25) =1/(25) (7 hat i+ 24 hat j)`
and pparallel to `vec B` is
`=|vec A| hat B = 5 xx 1/(25) (7 hat i + 24 hat j)`
`=1/5 (7 hat + 24 hat j)`1.