The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0, 2); (0, 4, 0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance 'r&#

Question

The position vectors of the four angular points of a tetrahedron OABC are (0, 0, 0); (0, 0, 2); (0, 4, 0) and (6, 0, 0) respectively. A point P inside the tetrahedron is at the same distance 'r' from the four plane faces of the tetrahedron. Find the value of 'r'.

TestHub · Accepted Answer

Equal distances to the coordinate planes give P=(r,r,r), with r positive because P is inside. The fourth face has intercepts 6,4,2. 6 x ​ + 4 y ​ + 2 z ​ = 1 , 2 x + 3 y + 6 z = 12. 2 2 + 3 2 + 6 2 ​ = 7. 7 12 − 11 r ​ = r , 18 r = 12 , r = 3 2 ​ . ​

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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