Question

The coordinates of four angular points of a tetrahedron are $(0,0,0),(0,0,2),(0,4,0)$ and $(6,0,0)$. A point $P$ inside the tetrahedron is at the same distance $r$ from the four plane faces of tetrahedron. Which of the following CANNOT be the value of $r$?

• A. $\frac{2}{3}$
• B. $\frac{2}{5}$
• C. $2$
• D. $3$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $\frac{2}{5}$
C $2$
D $3$

$P$ is a point equidistant from $ZX,XY$ and $YZ$ plane. So, coordinates of $P(r,r,r)$

Equation of the plane $ABC$ is -

$2x+3y+6z-12=0$

$r=\left|\frac{11r-12}{\sqrt{49}}\right|\Rightarrow r=3,\frac{2}{3}$

Since $r<2\Rightarrow r=\frac{2}{3}$