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(a x b) x c = (1/3)|b||c| a, no two collinear: sine of the angle between b and c

The same question, asked 4 times: 10 May 2023 S1*, 11 May 2023 S1, 16 May 2023 S1, 10 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    143
    Let a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} be three non-zero vectors such that no two of them are collinear and (a⃗×b⃗)×c⃗=13∣b⃗∣∣c⃗∣a⃗(\vec{a}\times\vec{b})\times\vec{c}=\frac{1}{3}|\vec{b}||\vec{c}|\vec{a}. If θ\theta is the angle between vectors b⃗\vec{b} and c⃗\vec{c}, then the value of cosec θ\text{cosec}\,\theta is

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  2. Question 2

    11 May 2023 S1

    127
    Let a, b and c be three non-zero vectors such that no two of them are collinear and (a⃗×b⃗)×c⃗=13∣b⃗∣∣c⃗∣a⃗(\vec{a}\times\vec{b})\times\vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}. If 'θ\theta' is the angle between the vectors b and c, then value of sin⁡θ\sin\theta is

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  3. Question 3

    16 May 2023 S1

    112
    Let a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} be three non-zero vectors such that no two of them are collinear and (a⃗×b⃗)×c⃗=13∣b⃗∣∣c⃗∣a⃗(\vec{a}\times\vec{b})\times\vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}. If θ\theta is the angle between vectors b⃗\vec{b} and c⃗\vec{c}, then the value of sin⁡θ\sin\theta is

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  4. Question 4

    10 May 2024 S1

    148
    (a⃗×b⃗)×c⃗=13∣b⃗∣∣c⃗∣a⃗(\vec{a}\times\vec{b})\times\vec{c}=\frac{1}{3}|\vec{b}||\vec{c}|\vec{a}. Angle θ\theta between b⃗\vec{b} and c⃗\vec{c}: value of sin⁡θ\sin\theta is

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