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Question 260013
JEE Mathematics · Hard

Vectors: Linear independence MCQ

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Linear independenceHardQuestion 260013

Question

Three vectors are linearly independent if:
  1. A
    Their scalar triple product ≠ 0
    Correct
  2. B
    They are mutually perpendicular only
  3. C
    Their sum is zero
  4. D
    They are unit vectors

Correct answer

Their scalar triple product ≠ 0

Explanation

Three vectors a⃗, b⃗, c⃗ are linearly independent iff [a⃗, b⃗, c⃗] ≠ 0 (non-zero scalar triple product). If [a⃗, b⃗, c⃗] = 0, they are coplanar (linearly dependent).

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