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AP EAMCET202423 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the angle between the line x+1 1 = y-1 2 = z-2 2 and the plane 2 x-y+ z+4=0 in such that = 1 3 , then the value of =

Options

  1. A3 / 5
  2. B5 / 4
  3. C5 / 3
  4. D4 / 3

Correct answer

C. 5 / 3

Step-by-step solution

( 2,-1, ) are the direction ratios perpendicular to the plane. (1,2,2) is the direction ratio of the line. Then, l = i +2 j +2 k and p =2 i - j + k Since, = l p | l | | p | = 2-2+2 3 5+ = 2 3 5+ = 2 3 5+ = 2 3 5+ 1 3 = 2 3 5+ 5+ =4 = 5 3 .

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