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|a|, |b|, |c|, |b x c| = sqrt(15) and b - 2c = lambda a: find lambda

The same question, asked 2 times: 16 May 2023 S2*, 12 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S2

    143
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three vectors such that a⃗≠0\vec{a} \neq 0 and a⃗×b⃗=2a⃗×c⃗\vec{a} \times \vec{b} = 2\vec{a} \times \vec{c}, ∣a⃗∣=∣c⃗∣=1|\vec{a}|=|\vec{c}|=1, ∣b⃗∣=4|\vec{b}|=4 and ∣b⃗×c⃗∣=15|\vec{b}\times\vec{c}|=\sqrt{15}. If b⃗−2c⃗=λa⃗\vec{b}-2\vec{c} = \lambda\vec{a}, then λ\lambda is

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  2. Question 2

    12 May 2024 S1

    101
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three vectors, ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=4|\vec{b}|=4, ∣c⃗∣=1|\vec{c}|=1, ∣b⃗×c⃗∣=15|\vec{b}\times\vec{c}|=\sqrt{15} and b⃗=2c⃗+λa⃗\vec{b}=2\vec{c}+\lambda\vec{a}, then the value of λ\lambda is

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