`||bbv|| = 5, bbu = ` Find the vector `bbv` with the given magnitude and the same direction as `bbu`.

The magnitude of a vector `u = a*i + b*j` , such that:

`|u| = sqrt(a^2+b^2)`

Since the problem provides the magnitude `|v| = 5` , yields:

`5 = sqrt(a^2+b^2)`

The direction angle of the vector can be found using the formula, such that:

`tan theta = b/a`

Since the problem provides the information that the direction angle of the vector v coincides to the direction angle of the vector `u = <2,5>` , yields:

`tan theta = 5/2 => b/a = 5/2> 5a = 2b => b = (5a)/2`

Replacing  `(5a)/2` for b in equation`5 = sqrt(a^2+b^2)` yields:

`5 = sqrt(a^2+25a^2/4)=> 25 = 29a^2/4 => 100 =29a^2 => a = +-10/(sqrt29)`

`b = +-25/(sqrt29)`

Hence, the component form of the vector v can be `<10/(sqrt29),25/(sqrt29)>` or `<-10/(sqrt29),-25/(sqrt29)>.`