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MHT CET202416 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

If the distance between the plane A x-2 y+ z = d and the plane containing the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-3 4 = z-4 5 is 6 units, then |d| is

Options

  1. A1
  2. B2
  3. C6
  4. D6

Correct answer

D. 6

Step-by-step solution

Equation of the plane containing the given lines is aligned & | array ccc x-1 & y-2 & z-3 2 & 3 & 4 3 & 4 & 5 array |=0 & (x-1)(15-16)-(y-2)(10-12) & +(z-3)(8-9)=0 aligned aligned & (x-1)(-1)-(y-2)(-2)+(z-3)(-1)=0 & -x+1+2 y-4-z+3=0 & -x+2 y-z=0 & x-2 y+z=0...(i) aligned Given equation of plane is A x-2 y+z=d...(ii) The planes given by equations (i) and (ii) are parallel. A=1 Distance between the planes ( D ) is aligned & D= | d 1^2+(-2)^2+1^2 |= | d 6 | & | d 6 |= 6 & |d|=6 aligned

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