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If a, b, c are non-coplanar vectors and λ is a real number, then [λ(a+b), λ²b, λc] = [a, b+c, b] holds for

1. exactly one real value of λ
2. no real value of λ
3. exactly three real values of λ
4. exactly two real values of λ

Correct answer: no real value of λ

Solution

The equation involves determinants of vectors, and since a, b, and c are non-coplanar, their determinant is non-zero. The left-hand side scales the vectors by powers of lambda, which cannot equal the linear combination on the right-hand side for any real lambda, indicating that there are no real solutions.

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