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MHT CET202123 Sep 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If A and B are the foot of the perpendicular drawn from the point Q ( a , b , c ) to the planes YZ and ZX respectively, then the equation of the plane through the points A , B , and O is (where O is the origin)

Options

  1. Ax a - y b - z c =0
  2. Bx a + y b - z c =0
  3. Cx a - y b + z c =0
  4. Dx a + y b + z c =0

Correct answer

B. x a + y b - z c =0

Step-by-step solution

From given data, we write A (0, ~b , c ) and B ( a , 0, c ) Equation of plane passing through A , B and O is aligned & | array lll x-0 & y-0 & z-0 0-0 & b-0 & c-0 a-0 & 0-0 & c-0 array |=0 | array lll x & y & z 0 & b & c a & 0 & c array |=0 & x(b c)-y(-a c)+z(-a b)=0 b c x+a c y-a b z=0 aligned Dividing both sides by abc, we get x a + y b - z c =0

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