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Unit vectors with a x (b x c) = k(b + c), b not parallel to c: angle between a and b

The same question, asked 5 times: 2 May 2023 S1*, 11 May 2023 S2, 11 May 2024 S1*, 13 May 2024 S2, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    127
    a⃗\vec{a}, b⃗\vec{b}, and c⃗\vec{c} are three unit vectors such that a⃗×(b⃗×c⃗)=32(b⃗+c⃗)\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\sqrt{3}}{2}(\vec{b} + \vec{c}). If b⃗\vec{b} is not parallel to c⃗\vec{c}, then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  2. Question 2

    11 May 2023 S2

    110
    Let a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} be three unit vectors such that a⃗×(b⃗×c⃗)=32(b⃗+c⃗)\vec{a}\times(\vec{b}\times\vec{c}) = \frac{\sqrt{3}}{2}(\vec{b}+\vec{c}). If b⃗\vec{b} is not parallel to c⃗\vec{c}, then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  3. Question 3

    11 May 2023 S2

    129
    If a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} are non-coplanar unit vectors such that a⃗×(b⃗×c⃗)=(b⃗+c⃗)2\vec{a}\times(\vec{b}\times\vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt{2}} then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  4. Question 4

    11 May 2024 S1

    146
    Let a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} be three unit vectors such that a⃗×(b⃗×c⃗)=32(b⃗+c⃗)\vec{a}\times(\vec{b}\times\vec{c})=\frac{\sqrt{3}}{2}(\vec{b}+\vec{c}). If b⃗\vec{b} is not parallel to c⃗\vec{c}, then the angle between a⃗\vec{a} and b⃗\vec{b} is

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  5. Question 5

    13 May 2024 S2

    112
    If a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c}, are non-coplanar unit vectors such that a⃗×(b⃗×c⃗)=b⃗+c⃗2\vec{a}\times(\vec{b}\times\vec{c})=\frac{\vec{b}+\vec{c}}{\sqrt{2}} then the angle between a⃗\vec{a} and b⃗\vec{b} is:

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  6. Question 6

    25 Apr 2025 S1

    144
    If aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} are non coplanar unit vectors such that a‾×(b‾×c‾)=b‾+c‾2\overline{a}\times (\overline{b}\times\overline{c}) =\frac{\overline{b}+\overline{c}}{\sqrt{2}} then the angle between a‾\overline{a} and b‾\overline{b} is

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