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BITSAT2023MathematicsVector AlgebraActual

A vector perpendicular to the plane containing the vectors i -2 j - k and 3 i -2 j - k is inclined to the vector i + j + k at an angle

Options

  1. A⁻¹ 14
  2. B⁻¹ 14
  3. C⁻¹ 15
  4. DNone of these

Correct answer

A. ⁻¹ 14

Step-by-step solution

A vector perpendicular to the plane is aligned & ( i -2 j - k ) (3 i -2 j - k ) & = | array ccc i & j & k 1 & -2 & -1 3 & -2 & -1 array |=-2 j +4 k & unit vector a = -2 j +4 k 4+16 = -2 j +4 k 2 5 aligned Angle between the unit vector and r = i + j + k = ⁻¹ r a | r | | a | = ⁻¹ 1 15 = ⁻¹ 14

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