a.)I What three points determine planes M, N and O?
The planes M, N, and O can be determined by any three non-collinear points on each plane. In other words, for plane M, three points A, B, and C that are not on a straight line can determine the plane. For plane N, three different points D, E, and F that are not on a straight line can determine the plane. And for plane O, three points G, H, and I that are not on a straight line can determine the plane.
b.) What are the intersections of planes M & N; planes N & O; and planes M & O?
The intersections of planes M and N, planes N and O, and planes M and O will depend on the relative positions of the planes in relation to each other.
If planes M and N intersect, their intersection will be a line (assuming they are not parallel).
If planes N and O intersect, their intersection will also be a line (assuming they are not parallel).
If planes M and O intersect, their intersection will be a point (assuming they are not parallel).
If any of the planes are parallel, they will not intersect and there will be no intersection line or point.
Answers & Comments
a.) I What three points determine planes M, N and O?
The planes M, N, and O can be determined by any three non-collinear points on each plane. In other words, for plane M, three points A, B, and C that are not on a straight line can determine the plane. For plane N, three different points D, E, and F that are not on a straight line can determine the plane. And for plane O, three points G, H, and I that are not on a straight line can determine the plane.
b.) What are the intersections of planes M & N; planes N & O; and planes M & O?
The intersections of planes M and N, planes N and O, and planes M and O will depend on the relative positions of the planes in relation to each other.
If any of the planes are parallel, they will not intersect and there will be no intersection line or point.
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