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MHT CET20226 Aug 2022Evening ShiftMathematicsThree Dimensional GeometryActual

A tetrahedron has vertices P (1,2,1), Q (2,1,3), R (-1,1,2) and O (0,0,0) . Then the angle between the faces OPQ and PQR is

Options

  1. A⁻¹ ( 17 35 )
  2. B⁻¹ ( 19 31 )
  3. C⁻¹ ( 19 35 )
  4. D⁻¹ ( 17 31 )

Correct answer

C. ⁻¹ ( 19 35 )

Step-by-step solution

Equation of OPQ is | array lll x & y & z 1 & 2 & 1 2 & 1 & 3 array |=0 5 x-y-3 z=0 equation of PQR is | array ccc x-1 & y-2 & z-1 2-1 & 1-2 & 3-1 -1-1 & 1-2 & 2-1 array |=0 x-5 y-3 z+12=0 Angle between the planes aligned & = ⁻¹ ( 5 1+(-1) (-5)+(-3) (-3) 5^2+(-1)^2+(-3)^2 1^2+(-5)^2+(-3)^2 ) & = ⁻¹ 19 35 35 = ⁻¹ ( 19 35 ) aligned

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