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MHT CET202619 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

From a point P (a, b, c) , perpendiculars PA and PB are drawn to XY plane and ZX plane respectively. If O is the origin, then the equation of plane OAB is

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

A. x a - y b - z c = 0

Step-by-step solution

The coordinates of point P are (a, b, c) . Since PA is perpendicular to the XY plane, the z -coordinate of A is 0 . Thus, the coordinates of A are (a, b, 0) . Since PB is perpendicular to the ZX plane, the y -coordinate of B is 0 . Thus, the coordinates of B are (a, 0, c) . The equation of the plane passing through the origin O (0, 0, 0) , A (a, b, 0) , and B (a, 0, c) is given by: vmatrix x & y & z a & b & 0 a & 0 & c vmatrix = 0 Expanding the determinant along the first row, we get: x(bc - 0) - y(ac - 0) + z(0 -

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