Travelling perpendicularly to the orbital plane of the solar system, also known as an escape trajectory, can indeed allow for faster travel out of the solar system compared to following the plane of the planets' orbits. This technique is commonly used in space exploration missions to maximize the spacecraft's velocity and achieve escape velocity more efficiently.
When a spacecraft follows a trajectory within the orbital plane, it must contend with the gravitational influences of the planets it passes, requiring complex maneuvers to gain sufficient velocity to escape the solar system. However, by moving out of the plane, the spacecraft can take advantage of a gravity-assist maneuver, often called a gravity slingshot or gravity assist.
A gravity assist involves using the gravity of a planet to increase or decrease the spacecraft's velocity. By carefully planning the trajectory and timing of the encounter with a planet, the spacecraft can gain a significant velocity boost without expending additional fuel. This technique allows the spacecraft to effectively "borrow" some of the planet's orbital energy and transfer it to its own trajectory.
When a spacecraft is on an escape trajectory and moves perpendicularly to the orbital plane, it can potentially encounter several planets for gravity assists, further increasing its speed. This approach enables the spacecraft to achieve higher velocities relative to the Sun and escape the solar system more efficiently than if it were confined to the orbital plane.
It's worth noting that reaching speeds necessary to leave the solar system entirely still requires significant amounts of energy and careful planning. Moreover, the choice of trajectory depends on mission objectives and the specific launch opportunities available at the time.