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JEE Main 2019 · 12 Jan · Shift I

JEE Main 2019 Mathematics question on Vector Algebra

The sum of the distinct real values of μ\mu, for which the vectors, μi^+j^+k^\mu\hat{i}+\hat{j}+\hat{k}, i^+μj^+k^\hat{i}+\mu\hat{j}+\hat{k}, i^+j^+μk^\hat{i}+\hat{j}+\mu\hat{k} are coplanar, is
  1. A.
    2
  2. B.
    0
  3. C.
    1
  4. D.
    −1-1
Show answer and solution

Correct option: D

Solution

For coplanarity, the determinant of the matrix formed by the three vectors must be zero:

|μ 1 1|
|1 μ 1| = 0
|1 1 μ|

Expanding: μ(μ²-1) - 1(μ-1) + 1(1-μ) = 0
= μ³ - μ - μ + 1 + 1 - μ = 0
= μ³ - 3μ + 2 = 0

Factor: (μ-1)²(μ+2) = 0, giving μ = 1 (repeated) and μ = -2.

The distinct real values are μ = 1 and μ = -2, and their sum is 1 + (-2) = -1.

[JEE Main 2019 · 12 Jan · Shift I]

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