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The intersection of three planes is either a point, a line, or there is no intersection if any two of the planes are parallel to each other. This tells us about possible solutions to 3 equations in 3 unknowns. There may be one solution, no solution, or infinite number of solutions.
Intersection of Medians-Centroid Intersection of Altitudes-Orthocentre
A volume.
Yes, it is possible for three distinct planes to intersect at a line.
centroid