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NDA2018MathematicsThree Dimensional GeometryActual

What is the equation of the plane passing through the points (-2,6,-6),(-3,10,-9) and (-5,0,-6) ?

Options

  1. A2 x-y-2 z=2
  2. B2 x+y+3 z=3
  3. Cx+y+z=6
  4. Dx-y-z=3

Correct answer

A. 2 x-y-2 z=2

Step-by-step solution

We know, the equation of plane passing through 3 points ( x ₁, y ₁, z ₁ ), ( x ₂, y ₂, z ₂ ) and ( x ₃, y ₃, z ₃ ) is | array ccc x - x ₁ & y - y ₁ & z - z ₁ x ₂- x ₁ & y ₂- y ₁ & z ₂- z ₁ x ₃- x ₁ & y ₃- y ₁ & z ₃- z ₁ array |=0 So, the plane passing through points (-2,6,-6) , (-3,10,-9) and (-5,0,-6) is aligned & | array ccc x +2 & y -6 & z +6 -1 & 4 & -3 -3 & -6 & 0 array |=0 & ( x +2)(-18)-( y -6)(-9)+( z +6)(6+12)=10 & -18 x -36+9 y -54+18 z +108=0 & -18 x +9 y +18 z +18=0 & 2 x - y -2 z -2=0 & 2 x - y -2 z =2

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