`||bbv|| = 2sqrt(3), theta = 45^@` Find the component form of `bbv` given its magnitude and the angle it makes with the positive x-axis.

You need to find the component form of the vector `v = <a,b>` , hence, you need to use the information provided.

You need to evaluate the magnitude |v|, such that:

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

`2sqrt3 = sqrt(a^2+b^2)`

The direction angle of the vector is `theta = 45^o` , hence, you may use the following formula:

`tan theta = b/a => tan 45^o = b/a => 1 = b/a => b = a`

Replacing a for b yields:

`2sqrt3 = sqrt(a^2+a^2) => 2sqrt3 = +-a*sqrt2 => a = +-sqrt6 => b = +-sqrt6`

Hence, evaluating the components of the vector v, yields `<sqrt6,sqrt6>` or `<-sqrt6,-sqrt6>.`