Is it possible for two points on the surface of a prism to be neither collinear nor coplanar?
You can always find a line and many planes to pass through two points. What does a prism have to do with it?
A prism is a three-dimensional figure with two identical parallel bases and rectangular sides connecting the bases. Each face of a prism is a parallelogram. In a prism, all points on the surface lie on one of the faces, and hence, they are coplanar.
Collinear means that the points lie on the same straight line. In the case of a prism, the points will always lie on the same face and hence, they will be collinear.
Thus, it is not possible for two points on the surface of a prism to neither be collinear nor coplanar. All points on the surface of a prism will be both collinear and coplanar.
No, it is not possible for two points on the surface of a prism to be neither collinear nor coplanar.
Collinear points are points that lie on the same straight line. In a prism, the faces are flat and planar, so any two points on the surface of a prism can be connected by a straight line that lies entirely within the same face. Therefore, they are collinear.
Coplanar points are points that lie on the same plane. In a prism, each face is a separate plane, so any two points on the surface of a prism will always lie on the same plane. Therefore, they are coplanar.
In summary, due to the nature of prisms and their planar faces, any two points on the surface of a prism will always be both collinear and coplanar.