GATE EE 2014 Set 1 — Question 10
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General Aptitude → Spatial Aptitude → 2D & 3D Patterns
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Question
When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines?
Correct answer
6 to 6
Solution
A tetrahedron has 4 vertices. Let the vertices be and , and the internal point be . Connecting to each vertex results in 4 straight lines: and . A plane is uniquely defined by any two intersecting lines. Since all four lines intersect at point , any pair of these lines will define a plane. The number of ways to choose 2 lines out of 4 is given by the combination formula:The 6 planes created are and . Because is an internal point, none of these planes coincide with the 4 original triangular faces of the tetrahedron (). Therefore, 6 new internal planes are created.
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