Question: An educator is using a STEM project to teach vector geometry. In a 3D coordinate system, a student plots three vertices of a regular tetrahedron: $A(1, 0, 0)$, $B(0, 1, 0)$, and $C(0, 0, 1)$. Find the integer coordinates of the fourth vertex $D$ such that all edges of the tetrahedron are of equal length.

Sun, 03 May 2026 03:32:58 +0000

Teaching Vector Geometry Through a 3D STEM Project: Finding the Fourth Vertex of a Regular Tetrahedron In modern STEM education, hands-on geometry projects bridge abstract mathematical concepts with real-world understanding. One compelling application is teaching vector geometry using 3D spatial reasoningÃƒÂ¢Ã‚Â€Ã‚Â”tasks like finding the missing vertex of a regular tetrahedron challenge students to apply coordinates, symmetry, and vector properties. A classic example involves plotting four points in 3D space to form a regular tetrahedron, where all edges are equal in length. This article explores a real classroom scenario where a STEM educator guides students through discovering the integer coordinates of the fourth vertex $D$ of a regular tetrahedron with given vertices $A(1, 0, 0)$, $B(0, 1, 0)$, and $C(0, 0, 1)$. --- ### What Is a Regular Tetrahedron?