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AP EAMCET202421 May 2024Morning ShiftMathematicsVector AlgebraActual

A (1,2,1), B (2,3,2), C (3,1,3) and D (2,1.3) are the vertices of a tetrahedron. If is the angle between the faces A B C and A B D then =

Options

  1. A5 14
  2. B15 8 7
  3. C3 14
  4. D5 2 7

Correct answer

D. 5 2 7

Step-by-step solution

(d) A (1,2,1), B (2,3,2), C (3,1,3) and D (2,1,3) Vector perpendicular to face ABC aligned & = AB AC & = AB AC = | array ccc i & j & k 1 & 1 & 1 2 & -1 & 2 array |=3 i -3 k aligned Vector perpendicular to face ABD = AB AD = | array ccc i & j & k 1 & 1 & 1 2 & -1 & 2 array |=3 i - j -2 k Angle between A B C and A B D = 9+6 18 14 = 15 3 28 = 5 2 7

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