It is like a hypothesis - a belief 9th house. Now it is time to test the hypothesis through experimentation 3rd house to validate or invalidate the hypothesis. Ketu 9th and Rahu 3rd here...
tuyet
What i got out of Ernst's teaching is the 9th house is Dharma and Jupiter represents purpose among many other things. We all have to move to Rahu and be comfortable with it so we can go back to Ketu house. We have to achieve the balance between the Axis. The opposite of the 3rd house is the 9th house, the house of self. Discover your purpose, your true self, your belief then test it to see if what you believe in is true. Test your purpose in life. 9th house is the process of seeing ourselves in a greater height, higher self-discovery. Walk along your path in what you believe and see where it takes you in your life journey. You will gain more wisdom and figure new things out. Trust your intelligence which is the 3rd house to transition what you know into something new. It may work or it may not work but at least you test it and put into practical use. That is the 9th house. To me that is what exploring Rahu house is all about...
3rd house is the house of will and efforts. Having Ketu in the 3rd house is a good position because that is an asset to the chart. If you have strong will once you put your mind into doing something you will have a capability to achieve great things.
You may want to look at the lord or Rahu and Ketu to see the dignity and avastha to assess the chart as a whole...
tuyet
Well as someone who has rahu in 3rd, and ketu in 9th, I would say that its a long interpersonal journey to find what one truly cherishes and values, all in a form of spiritualization on all levels that must be in balance. This is even more confounded when they are specifically in capricorn and cancer, and I am a scorpio ascendant. In my case in point, its also more about deep spiritualization since ketu is with jupiter and jupiter rules Sagittarius, and both the moon and saturn are in those ruled houses with saturn being in Sagittarius ruling Capricorn. My nakshutra further pushes that.