Recently I found [this tutorial video][1] about Jet streaks. Originally I was looking for the topic because of a particular problem I have to solve but now I got stuck here:.

[![enter image description here][2]][2]

Mathematically it is clear for me that ageostrophic wind calculates according to

$$\vec v_{ag} = \frac{1}{f} \cdot \vec k \times \frac{d \vec v}{d t}$$ 

But now my problem:

It is assumed that the real wind flows in x direction from W to (blue) E. Therefore, the ageostrophic wind is oriented towards north direction (green arrow). But, vectorially, this means that the geostrophic wind (red) must be directed a little to south so that read + green = blue.

But isn't that in contradiction to the fact, that geostrophic wind is always oriented along contours of constant height? Especially in this image, the contour through the point of interest is the straight line from W to E and not oriented towards south.

What is wrong in my understanding? 

  [1]: https://www.youtube.com/watch?v=svke_051zzc
  [2]: https://i.sstatic.net/bunqU.png