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AP EAMCET202419 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

A line L passes through the points (1,2,-3) and (3,3-1) and a plane passes through the points (2,1,-2),(-2,-3,6) , (0,2,-1) . If is the angle between the line L and plane , then 27 ^2 =

Options

  1. A25
  2. B9
  3. C5
  4. D2

Correct answer

D. 2

Step-by-step solution

Since equation of line L is x-1 2 = y-2 1 = z+3 2 and equation of the plane is | array ccc x-2 & y-1 & z+2 -2-2 & -3-1 & 6+2 0-2 & 2-1 & -1+2 array |=0 x+y+z=1 Now, angle between line and plane is given by aligned & = | 1 2+1 1+2 1 1+1+1 2^2+1+2^2 |= 5 3 3 & ^2 = 25 27 ^2 = 2 27 & 27 ^2 =2 . aligned

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