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NDA2015MathematicsThree Dimensional GeometryActual

A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively. What is the equation of plane ABC?

Options

  1. Ax+2 y+3 z=1
  2. B3 x+2 y+z=3
  3. C2 x+3 y+6 z=18
  4. D6 x+3 y+2 z=18

Correct answer

D. 6 x+3 y+2 z=18

Step-by-step solution

The plane passes through the point A (3,0,0), B (0,6,0) and C(0,0,9) . So, it should satisfy the equation given in option for all the three points. From option (A) For point A (3,0,0)x+2 y+3 z=1 array ll & 3+0+0 1 & option (A) is wrong. & From option (B) & For point A(3,0,0) & 3 x +2 y + z =3 & 3(3)+0+0 3 & option (B) is wrong. & From option (C) & For point A (3,0,0) & 2 x +3 y +6 z =18 & 2(3)+0+0 18 & option ( C ) is wrong. & From option ( D ) & For point A (3,0,0) & 6 x +3 y +2 z =18 array array ll & 6(3)+0+0=18

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