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Q.

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. If a point P inside the tetrahedron is at equal distances ‘r’ from the four planes of the tetrahedron, then the value of 3r is

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a

2

b

8

c

9

d

4

answer is B.

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Detailed Solution

Clearly three planes of the tetrahedron are coordinate planes, the fourth plane ABC is $2 x + 3 y + 6 z = 12$ ; let P(r,r,r) be given point.
Given $| \frac{2 r + 3 r + 6 r - 12}{\sqrt{4 + 9 + 36}} | = r$
$\Rightarrow r = \frac{2}{3} o r 3$
Since P-lies inside, $r \neq 3$ $∴ r = \frac{2}{3}$

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