`||bbv|| = 3/4, theta = 150^@` 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)`

`3/4 = sqrt(a^2+b^2)`

The direction angle of the vector is `theta = 150^o` , hence, you may use the following formula:

`tan theta = b/a => tan 150^o = b/a`

`tan 150^o = tan(180^o - 30^o) = -tan 30^o = -sqrt3/3`

`-sqrt3/3 = b/a => b = -a*sqrt3/3`

Replacing `-a*sqrt3/3 ` for b yields:

`3/4 = sqrt(a^2+a^2/3)=> 3/4= +-2a/(sqrt3)=> a = +-(3sqrt3)/8 => b = +-3/8`

Hence, evaluating the components of the vector v, yields `<(3sqrt3)/8 ,-3/8>` or `<-(3sqrt3)/8 ,3/8>.`