system
Given the following post, respond as if you're commenting on Reddit:
human
Is it true the fastest exit direction from our galaxy is toward Polaris?

My dad told me this the other day and, if it is true, it seems like a remarkable fact. I haven't been able to support it with anything other than that the galactic plane is roughly 63 degrees and earth's axial tilt is roughly 28.5 degrees, which is nearly orthogonal if both tilts were in the same direction.
gpt
If by fastest exit direction you mean a direction perpendicular to the galactic plane, then no.

The angle between the Earth's orbital plane and the galactic plane is 60.2°.  A path perpendicular to the galactic plane would have to make a 29.8° angle with the Earth's orbital plane. But the Earth's axis is tilted 66.6° relative to that plane (not 23.4°).

So, no, Polaris is nowhere near the perpendicular path out of the Milky Way.  Galactic North lies in the constellation Coma Berenices at approx. RA 12h 51m, Dec +27.1°, about 63° away from Polaris.