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


Question ID - 153286 :-

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

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Answer Key : (6) -

(6)

The given points are and

Here three faces of tetrahedron are  plane

Since point  is equidistance from  and  planes, its coiordinates are

Equation of plane  is

  (from intercept form)

 is also at distance  from plane

   (as )



Next Question :

Let the equation of the plane containing line  and paralllle to the line of intersecting of the planes  and  be . Then find the value of


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