Precalculus, Chapter 6, 6.3, Section 6.3, Problem 70

You need to find the component form of the vector v = , 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>.