true
true
A cone needs a three dimensional space in which to exist but it's not a solid, it's a two dimensional surface.
Cone
A triangle is a two dimensional shape with three straight lines and three vertices. A sphere is a three dimensional object with no straight lines and no vertices and such that every point on its surface is a constant distance from a fixed point. It is not possible to have a triangle sphere.
Yes, it does exist.
true
true
true
The term "statue" is used for three-dimensional works of art. Of course, two-dimensional works of art exist, but they are not usually called "statues".
A 3D triangle
There are a number of three dimensional shapes. These include the cube, the square pyramid, the prism, as well as the rhombohedron.
vertex
A cone needs a three dimensional space in which to exist but it's not a solid, it's a two dimensional surface.
A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
Three-dimensional things are objects that have height, width, and depth. They exist in physical space and have the ability to be viewed from multiple angles. Examples include a cube, sphere, and pyramid.
Presumably, the "three dimensional triangular plane" is actually a two dimensional plane which is "tilted" with respect to the axes. The point of intersection is simply the coordinates of the solution to the simultaneous equations for the line and the plane.