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MHT CET2019Evening ShiftMathematicsThree Dimensional GeometryActual

If the foot of the perpendicular drawn from the point (0,0,0) to the plane is (4, -2, -5) then the equation of the plane is …..

Options

  1. A4 x + 2 y + 5 z = - 13
  2. B4 x - 2 y - 5 z = 45
  3. C4 x + 2 y - 5 z = 37
  4. D4 x - 2 y + 5 z = - 5

Correct answer

B. 4 x - 2 y - 5 z = 45

Step-by-step solution

We have, foot of the perpendicular drawn from the point (0,0, 0) to the plane is (4, -2, -5). ∴ Direction ratios of normal to the required plane is 0 - 4,0 + 2,0 + 5) i . e (- 4,2 , 5 ∴ Required equation of plane passing through (4, -2, 5) is a x - x 1 + b y - y 1 + c z - z 1 = 0 ⇒ - 4 x - 4 + - 2 y + 2 + 5 z + 5 = 0 ⇒ - 4 x + 2 y + 5 z + 16 + 4 + 25 = 0 ⇒ 4 x - 2 y - 5 z = 45

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