`||bbv|| = 4sqrt(3), theta = 0^@` Find the component form of `bbv` given its magnitude and the angle it makes with the positive x-axis.

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| = 4sqrt3` , yields:

`4sqrt3= 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 is `theta = 0^o` , yields:

`tan 0^o = b/a => b = 0, a!=0`

Replacing  0 for b in equation `4sqrt3= sqrt(a^2+b^2)` yields:

`4sqrt3= sqrt(a^2+0)=> a = +-4sqrt3`

`b = 0`

Hence, the component form of the vector v can be `<4sqrt3,0>` or `<-4sqrt3,0>.`