It would depend upon your coordinate system. But in the regular Cartesian (rectangular) coordinate system you used in high school, the x axis is left to right and the y axis is up and down. So the vertical plane would be the xy plane.
If you are in three dimensions, the x axis is forward and backwards (coming out of the page toward and away from you), the y axis is left and right, and the z axis is up and down. So you would have two vertical planes--the xz plane and the yz plane.
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No, horizontal planes run parallel to each other, so they do not intersect, but two vertical planes can intersect. Imagine the pages of a books as several planes. When you stand the book up, they are all vertical, but they all intersect at the book spine.
There are many possible answers: A cylinder A cone sliced by two planes perperndicular to its axis A toroid (doughnut) sliced by a plane vertical to its axis. A sphere sliced by two planes An ellipsoid sliced by two planes A paraboloid sliced by two planes etc.
They are mutually perpendicular. However, they need not intersect: if they are in different planes, they will not intersect.
If a two-dimensional shape has a line of symmetry, the shape is also symmetrical with respect to the plane passing through that line and perpendicular to the plane of the shape. For example, the floor of a rectangular room is symmetrical about a vertical plane halfway along the length (or breadth) of the room. Some 3-dimensional shapes will also have planes of symmetry. A sphere has infinitely many. An ellipsoid has three - one each along two of its axes. A cuboid, similarly, has 3. A torus (doughnut) has one. A pyramid with a n-gon base will have n vertical planes, and so on.
-- the Boeing 787 wing-- the helicopter rotor-- the submarine diving planes-- the vertical people-movers in the Sears tower-- Pamela Anderson