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JEE Main2003MathematicsThree Dimensional GeometryActual

Two system of rectangular axes have the same origin. If a plane cuts them at distances a , b , c and a ^ , b ^ , c ^ from the origin then

Options

  1. A1 a^2 + 1 b^2 + 1 c^2 - 1 a^ 2 - 1 b^ 2 - 1 c^ 2 =0
  2. B1 a^2 + 1 b^2 + 1 c^2 + 1 a²² + 1 b²² + 1 c²² =0
  3. C1 a ^2 + 1 ~b ^2 - 1 c ^2 + 1 a ^ 2 + 1 ~b ^ 2 - 1 c ^ 2 =0
  4. D1 a^2 - 1 b^2 - 1 c^2 + 1 a^ 2 - 1 b^ 2 - 1 c^ 2 =0

Correct answer

A. 1 a^2 + 1 b^2 + 1 c^2 - 1 a^ 2 - 1 b^ 2 - 1 c^ 2 =0

Step-by-step solution

Eq. of planes be x a + y b + z c =1 & x a ₁ + y b ₁ + z c ₁ =1( r distance on plane from origin is same. ) | -1 1 a ^2 + 1 ~b ^2 + 1 c ^2 |= | -1 1 a ₁^2 + 1 ~b ₁^2 + 1 c ₁^2 | 1 a^2 - 1 a₁^2 =0

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