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KCET2023MathematicsThree Dimensional Geometry

The equation of the plane through the points (2,1,0),(3,2,-2) and (3,1,7) is

Options

  1. A2 x-3 y+4 z-27=0
  2. B6 x-3 y+2 z-7=0
  3. C7 x-9 y-z-5=0
  4. D3 x-2 y+6 z-27=0

Correct answer

C. 7 x-9 y-z-5=0

Step-by-step solution

We know that the equation of a plane passing through three non-collinear points. (x₁, y₁, z₁ ), (x₂, y₂, z₂ ) and (x₃, y₃, z₃ ) | array lll x-x₁ & y-y₁ & z-z₁ x₂-x₁ & y₂-y₁ & z₂-z₁ x₃-x₁ & y₃-y₁ & z₃-z₁ array |=0 aligned & | array ccc x-2 & y-1 & z-0 3-2 & 2-1 & -2-0 3-2 & 1-1 & 7-0 array |=0 & | array ccc x-2 & y-1 & z 1 & 1 & -2 1 & 0 & 7 array |=0 & (x-2)(7-0)-(y-1)(7+2)+z(0-1)=0 & 7 x-14-(y-1) 9+(-z)=0 & 7 x-9 y-z-5=0 aligned

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