No, the solar system is not on the same plane as the galaxy. The solar system refers specifically to our Sun and the celestial bodies that orbit it, including planets, moons, asteroids, and comets. The solar system is located within the Milky Way galaxy, which is a vast collection of stars, gas, dust, and other celestial objects.
The Milky Way galaxy is a spiral galaxy, and its disk-like structure is roughly flat, with a central bulge and spiral arms extending outwards. The solar system is located within the disk of the Milky Way, but it is not perfectly aligned with the galactic plane.
The solar system is tilted at an angle of about 60 degrees with respect to the galactic plane. This means that as the solar system orbits the center of the galaxy, it moves above and below the galactic plane. It takes the solar system around 225-250 million years to complete one orbit around the center of the Milky Way.
So, while the solar system and the galaxy share a general disk-like structure, they are not on the exact same plane.