#### 17Question: Given three vertices of a cube at $(0, 0, 0)$, $(1, 0, 0)$, and $(0, 1, 0)$, find the coordinates of the fourth vertex in the same face, assuming all coordinates are integers and the cube has edge length 1.

Fri, 17 Apr 2026 05:56:10 +0000

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**#### 17Question: Given three vertices of a cube at $(0, 0, 0)$, $(1, 0, 0)$, and $(0, 1, 0)$, find the coordinates of the fourth vertex in the same face, assuming all coordinates are integers and the cube has edge length 1.** People are increasingly exploring 3D geometry fundamentals—especially in education, design, and problem-solving—driven by growing interest in spatial reasoning and STEM learning. Understanding cube structures like this one is a key building block in visual literacy, influencing fields from architecture to tech and gaming. As curiosity spikes around interactive models and digital design tools, mastering basic cube geometry becomes essential for guided exploration. This question isn’t just a math exercise—it reflects a common challenge in visual puzzle-solving: identifying a missing corner from three known points on the same flat face. Given these three vertices, all located at integer coordinates and forming a plane aligned with the xy-plane at z = 0, the geometry of a unit cube clarity becomes apparent. ### Why This Cube Face Problems Matter Now