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JEE Main201912 Jan 2019Morning ShiftMathematicsVector AlgebraActual

The sum of the distinct real values of μ for which the vectors μ i ^ + j ^ + k ^ , i ^ + μ j ^ + k ^ , i ^ + j ^ + μ k ^ are co-planar, is

Options

  1. A0
  2. B- 1
  3. C1
  4. D2

Correct answer

B. - 1

Step-by-step solution

Given the three vectors are coplanar. Hence, μ 1 1 1 μ 1 1 1 μ = 0 ⇒ μ μ 2 - 1 - 1 μ - 1 + 1 1 - μ = 0 ⇒ μ μ - 1 μ + 1 - 2 μ - 1 = 0   ∵ a 2 - b 2 = a - b a + b ⇒ μ − 1 μ   μ + 1 − 2 = 0 ⇒ μ − 1 μ 2 + μ + 2 = 0 ⇒ μ − 1 μ - 1 μ + 2 = 0 ⇒ μ = 1 ,   1 ,   - 2 Therefore, the sum of the distinct real values of μ = - 2 + 1 = - 1

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