Q: Is a plane determined by a point and a line?

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point, line and plane

A ray

When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.

Point ; Line ; Plane - Remember the Point-Line-Plane Postulate

The line and the point define a plane.

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Yes, three points determine a plane unless they are in a straight line. A plane is two dimensions a line is only one. You need a third point(not in the line) to define a plane.

Plane. A point has no dimension, a line has one dimension, and a plane has two dimensions.

point, line and plane

point * * * * * or, nothing (if the line is parallel to the plane).

A ray

plane

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 plane.

plane

A plane intersects a line at a point, and i plane intersects another plane at a line.

When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.

Unless the line is a subset of the plane, the intersection is a point.