Question

A plane intersects the co ordinate axes at $A,B,C$. If $O=(0,0,0)$ and $(1,1,1)$ is the centroid of the tetrahedron $OABC$, then the sum of the reciprocals of the intercepts of the plane

• A. $12$
• B. $\frac{4}{3}$
• C. $1$
• D. $\frac{3}{4}$

Answer 1

The correct option is D $\frac{3}{4}$

Let the point of intersections be,
$A(a,0,0),B(0,b,0)$ and $C(0,0,c)$
The coordinates of the centroid are $(\frac{a}{4},\frac{b}{4},\frac{c}{4})$
Comparing it with the coordinates given, we get
$a=4,b=4,c=4$
Hence, $(\frac{1}{a},\frac{1}{b},\frac{1}{c})=\frac{3}{4}$