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|a + b + c| = 1, c = lambda(a x b), |a| = 1/sqrt(3), |b| = 1/sqrt(2), |c| = 1/sqrt(6): angle between a and b

The same question, asked 2 times: 14 May 2024 S1, 20 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S1

    125
    If a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} are three vectors such that ∣a⃗+b⃗+c⃗∣=1|\vec{a}+\vec{b}+\vec{c}|=1, c⃗=λ(a⃗×b⃗)\vec{c}=\lambda(\vec{a}\times\vec{b}) and ∣a⃗∣=13|\vec{a}|=\dfrac{1}{\sqrt{3}}, ∣b⃗∣=12|\vec{b}|=\dfrac{1}{\sqrt{2}}, ∣c⃗∣=16|\vec{c}|=\dfrac{1}{\sqrt{6}}, then the angle between a⃗\vec{a} and b⃗\vec{b} is:

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  2. Question 2

    20 Apr 2026 S1

    92
    If aˉ,bˉ\bar{a}, \bar{b} and cˉ\bar{c} are three vectors such that ∣aˉ+bˉ+cˉ∣=1,cˉ=λ(aˉ×bˉ)|\bar{a} + \bar{b} + \bar{c}| = 1, \bar{c} = \lambda(\bar{a} \times \bar{b}) and ∣aˉ∣=13,∣bˉ∣=12,∣cˉ∣=16|\bar{a}| = \dfrac{1}{\sqrt{3}}, |\bar{b}| = \dfrac{1}{\sqrt{2}}, |\bar{c}| = \dfrac{1}{\sqrt{6}}, then the angle between aˉ\bar{a} and bˉ\bar{b} is

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