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Three vectors a, b, c satisfy a≠ 0 and a×b=2 a×c. Also, |a|=|c|=1, |b|=4, and the angle between b and c is cos⁻¹ ((1)/(4)). If b-2c=λ a, then the value of λ is

1. ± 2
2. ± 4
3. 1/2
4. 1/4

Correct answer: ± 4

Solution

The equation ( ext{b} - 2 ext{c} = ext{λa} ext{ implies that the vector ( ext{b} - 2 ext{c} ext{ is parallel to ( ext{a} ext{. Given the magnitudes and the relationship between the vectors, we find that ( ext{λ} ext{ must equal ( ext{±4} ext{ to satisfy the conditions of the problem, particularly the magnitudes and the angle between ( ext{b} ext{ and ( ext{c} ext{.

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