The problem asks me to find a unit vector in the direction of the given vector. The problem is w=i-2j and another is w=2j.

Yes, that's it. For example, if you have


\vec w = 3\hat i + 4 \hat j


the magnitude of this vector |\vec w | is 5. (Here \hat i and \hat j are the unit vectors in the x ans y directions, respectively.) So the unit vector would be:


\vec w = \frac 3 5 \hat i + \frac 4 5 \hat j