Maths · Scalar and vector products
If are non-coplanar vectors and is a real number, then \lambda^{2} \vec{b} \lamb
If \( a, b, c \) are non-coplanar vectors and \( \lambda \) is a real number, then \( \left[\lambda(\vec{a}+\vec{b}) \lambda^{2} \vec{b} \lambda \vec{c}\right]=[\vec{a} \quad \vec{b}+\vec{c} \quad \vec{b}] \) for
- A. exactly two values of \( \lambda \)
- B. exactly three values of \( \lambda \)
- C. no value of \( \lambda \)
- D. exactly one value of \( \lambda \)
Step-by-step solution
The scalar triple product equality simplifies to λ^4 (a·(b×c)) = -a·(b×c). Since a, b, c are non-coplanar, a·(b×c) ≠ 0, so λ^4 = -1, which has no real solution. Hence no λ satisfies the equation.
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