Three Dimensional Geometry Question 305
Question: If a plane meets the co-ordinate axes at A,B and C such that the centroid of the triangle is (1, 2, 4) then the equation of the plane is
[Kerala (Engg.) 2005]
Options:
A) $ x+2y+4z=12 $
B) $ 4x+2y+z=12 $
C) $ x+2y+4z=3 $
D) $ 4x+2y+z=3 $
E) $ x+y+z=12 $
Show Answer
Answer:
Correct Answer: B
Solution:
Given, plane meets the co-ordinate axes at $ A(a,0,0),B(0,b,0)C(0,0,c) $ \ Centroid $ \equiv ( \frac{a}{3},\frac{b}{3},\frac{c}{3} )=(1,,2,,4) $
Þ $ a=3,b=6,c=12 $ Hence, equation of required plane is, $ \frac{x}{3}+\frac{y}{6}+\frac{z}{12}=1 $
Þ $ 4x+2y+z=12 $ .
BETA
