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AP EAMCET20224 Jul 2022Morning ShiftMathematicsThree Dimensional GeometryActual

The x -intercept of a plane π passing through the point 1 , 1 , 1 is 5 2 and the perpendicular distance from the origin to the plane π is 5 7 . If the y -intercept of the plane π is negative and the z -intercept is positive then its y -intercept is

Options

  1. A- 5 3
  2. B- 5 6
  3. C- 3 2
  4. D- 5 2

Correct answer

A. - 5 3

Step-by-step solution

Let the equation of plane be x a + y b + z c = 1 Now given a = 5 2 So, equation becomes 2 x 5 + y b + z c = 1 Now given plane passes through 1 , 1 , 1 ⇒ 2 5 + 1 b + 1 c = 1 ⇒ 1 b + 1 c = 3 5 Now given distance from origin is 5 7 So by formula we get, 1 4 25 + 1 b 2 + 1 c 2 = 5 7 ⇒ 4 25 + 1 b + 1 c 2 - 2 b c = 7 5 Now using value of 1 b + 1 c = 3 5 we get, ⇒ b c = - 25 18             . . . 1 & 1 b + 1 c = 3 5 ⇒    b + c b c = 3 5 ⇒  &#1

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