Introduction to 3D coordinate geometry — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSIntroduction to 3D coordinate geometry4 Marks
Question
Prove that the tetrahedron with vertices at the points O(0, 0, 0), A(0, 1, 1), B(1, 0, 1) and C(1, 1, 0) is a regular one.
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Answer
Here, $\text{AB}=\sqrt{(0-1)^2+(1-0)^2+(1-1)^2}$ $=\sqrt{1+1}$ $=\sqrt{2}\text{ units}$ $\text{BC}=\sqrt{(1-1)^2+(0-1)^2+(1-0)^2}$ $=\sqrt{1+1}$ $=\sqrt{2}\text{ units}$ $\text{CA}=\sqrt{(1-0)^2+(1-1)^2+(0-1)^2}$ $=\sqrt{1+0+1}$ $=\sqrt{2}\text{ units}$ $\text{DA}=\sqrt{(0-0)^2+(0-1)^2+(0-1)^2}$ $=\sqrt{1+1}$ $=\sqrt{2}\text{ units}$ $\text{OB}=\sqrt{(0-1)^2+(0-0)^2+(0-1)^2}$ $=\sqrt{1+1}$ $=\sqrt{2}\text{ units}$ $\text{DA}=\sqrt{(0-1)^2+(0-1)^2+(0-0)^2}$ $=\sqrt{1+1}$ $=\sqrt{2}\text{ units}$ Since, OA = OB = OC = AB = BC = CA So, O, A, B, C represent a regular tetrahedron.
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