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

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, $ x+2 y+4 z=12 $, $ 4 x+2 y+z=12 $, $ x+2 y+4 z=3 $, $ 4 x+2 y+z=3 $

MARKS App · Accepted Answer

Given plane meets the co-ordinate axes at A a , 0,0 , B 0 , b , 0 C 0,0 , c G = Centroid ≡ a 3 , b 3 , c 3 = 1 , 2 , 4 a = 3 , b = 6 , c = 12 Hence, equation of required plane is, x 3 + y 6 + z 12 = 1 4 x + 2 y + z = 12 .

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