In which direction does the ecliptic plane make an angle of 63 degrees with galactic plane? Is it toward the galactic center? (It can have any 360 degree orientation.)
The line defining where the ecliptic plane and the Galactic plane coincide lies (approximately) between the points defined by right ascensions and declinations of 6h +23 and 18h -23.
This can be seen below - the plot is in celestial coordinates with the ecliptic plane marked (thicker solid line) and the Galactic plane clearly visible in the background map of dust extinction.
The second of these coordinates is close to, but not coincident, with the Galactic centre (marked Sgr A*). So the relative tilt is sort of at right angles to the Galactic centre at present.
Of course this will change over tens of millions of years as the solar system orbits the Galaxy.