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|a| = 1, |b| = 4, a.b = 2 and c = 2(a x b) - 3b: angle between b and c

The same question, asked 2 times: 9 May 2024 S2, 20 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    9 May 2024 S2

    125
    Vectors a⃗\vec{a} and b⃗\vec{b} are such that ∣a⃗∣=1|\vec{a}|=1, ∣b⃗∣=4|\vec{b}|=4 and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2. If c⃗=2a⃗×b⃗−3b⃗\vec{c} = 2\vec{a}\times\vec{b} - 3\vec{b}, then the angle between b⃗\vec{b} and c⃗\vec{c} is

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  2. Question 2

    20 Apr 2025 S1

    113
    Let aˉ\bar{a} and bˉ\bar{b} be two vectors such that ∣a‾∣=1,∣ b‾∣=4,a‾⋅b‾=2|\overline{a}| = 1,|\overline{\text{ }b}| = 4,\overline{a}\cdot\overline{b}= 2. If c‾=(2a‾×b‾)−3 b‾\overline{c}= (2\overline{a}\times\overline{b}) - 3\overline{\text{ }b}, then the angle between b‾\overline{b} and c‾\overline{c} is

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