Let the vectors a = (1 + t) i + (1 - t) j + k , b = (1 - t) i + (1 + t) j + 2 k and c = t i - t j + k , t R be such that for , , R, a + b + c = 0 = = = 0. Then the set of all values of t is -

JEE Main 2022 Mathematics question

Let the vectors , and , t R be such that for , , R, . Then the set of all values of t is -

Answer: (C)

The condition means that , , are linearly independent (non-coplanar), i.e. the determinant |1 + t, 1 − t, 1; 1 − t, 1 + t, 2; t, −t, 1| .

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Question ID VK-034778