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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

The position vectors of the angular points of a tetrahedron are A(3 i -2 j + k ), B(3 i + j +5 k )C(4 i +3 k ) and D( i ) . Then the acute angle between the lateral face ADC and the base face A B C is:

Options

  1. A⁻¹ 5 2
  2. B⁻¹ 2 5
  3. C⁻¹ 1 5
  4. D2 ⁻¹ ( 2+ 25 5 )

Correct answer

D. 2 ⁻¹ ( 2+ 25 5 )

Step-by-step solution

A D =-2 i +2 j - k , A C = i +2 j +2 k vector perpendicular to the face A D C is = | array ccc i & j & k -2 & 2 & -1 1 & 2 & 2 array |=6 i +3 j -6 k A B =3 j +4 k A vector perpendicular to the face A B C is = | array lll i & j & k 0 & 3 & 4 1 & 2 & 2 array |=-2 i +4 j -3 k acute angle between the two faces is given by = | -12+12+18 36+9+36 4+16+9 |= 2 29 aligned & = 5 2 & = ⁻¹ 5 2 aligned

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