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MHT CET202522 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of the plane r =( i - j )+ ( i + j + k )+ ( i -2 j +3 k ) from the origin is

Options

  1. A7 38 units
  2. B1 38 units
  3. C5 38 units
  4. D2 38 units

Correct answer

A. 7 38 units

Step-by-step solution

The plane's distance from the origin is determined by converting its vector equation to standard form and applying the distance formula. The plane equation r = ( i - j ) + ( i + j + k ) + ( i -2 j +3 k ) indicates a normal vector n = b c = 5 i - 2 j - 3 k . Since point i - j lies on the plane, the scalar constant evaluates to d = a n = 7 . The Cartesian form becomes 5x - 2y - 3z = 7 . The distance from the origin to this plane is given by |7| 5^2 + (-2)^2 + (-3)^2 = 7 38 units. Final answer: 7 38 units

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