A ray
Line, Ray and segment
Plane.
If on your paper your answers are point, ray, line segment, or plane i think it will be Plane
A ray is a dot at one end of the line and a arrow at the other end.
The vertex is the intersection of the rays that form an angle. The other ends go on indefinitely.
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.
A line or a ray - depending on whether the planes are finite or infinite.
A ray
Not in plane Euclidean geometry.
A ray is not an undefined term.
Line, Ray and segment
line
Plane.
A right angle.
If on your paper your answers are point, ray, line segment, or plane i think it will be Plane
None of them since a thread has a finite length and finite width. A point has neither length nor width whereas a line, line segment and ray do not have any width. A plane has infinite length and width. The nearest approximation is a line segment.