The number of distinct real values of for which the vectors - ^2 i+ j+ k, i+ ^2 j+ k and, i+ j- ^2 k are coplanar, is

MHT CET 2024 Mathematics question

The number of distinct real values of for which the vectors and, are coplanar, is

Answer: (A)

Three vectors are coplanar iff their scalar triple product (determinant) is zero. Let : . So we need . The quadratic has discriminant ,

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Question ID VK-093424