The long one, with the red scabbard, is the famous nodachi of Sasaki Kojiro, nickname Monohoshizao "Laundry-Drying Pole". The blade is 90 cm long, about 20 cm longer that a regular katana.
The sword with the black scabbard was the one owned by Miyamoto Musashi, and is is good to know that the original still exists, being displayed at the Shimada Museum of Arts in Kumamoto. However, Musashi hasn't used it in the duel with Sasaki Kojiro - he was armed with a wakizashi and a very long, probably 110 cm bokken (wooden sword).
EXIF info:
Nikon Df
Lens: 24-70mm F/2.8G
Focal Length: 24mm
Aperture: F/5
Shutter Speed: 1/60s
ISO Sensitivity: ISO 2000