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Angle between vectors from an equation in a vector triple product such as a x (b x c) = k(b + c)

This type of question, asked 12 times: 2 May 2023 S1, 10 May 2023 S1, 11 May 2023 S1, 11 May 2023 S2, 16 May 2023 S1, 10 May 2024 S1, 11 May 2024 S1, 13 May 2024 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S2, 14 May 2026 S2. All 13 questions 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

    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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  3. Question 3

    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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  4. Question 4

    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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  5. Question 5

    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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  6. Question 6

    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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  7. Question 7

    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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  8. Question 8

    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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  9. Question 9

    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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  10. Question 10

    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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  11. Question 11

    25 Apr 2025 S2

    132
    If b‾\overline{b} and c‾\overline{c} are unit vectors and ∣a‾∣=7|\overline{a}| = 7, a‾×(b‾×c‾)+b‾×(c‾×a‾)=12a‾\overline{a}\times (\overline{b}\times\overline{c}) +\overline{b}\times (\overline{c}\times\overline{a}) =\frac{1}{2}\overline{a}, then angle between the vectors aˉ\bar{a} and cˉ\bar{c} and angle between the vectors bˉ\bar{b} and cˉ\bar{c} are respectively

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  12. Question 12

    13 Apr 2026 S2

    92
    If aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} are three non zero and non-coplanar vectors such that aˉ×(bˉ×cˉ)=bˉ2\bar{a} \times (\bar{b} \times \bar{c}) = \dfrac{\bar{b}}{2}, then the angle between aˉ\bar{a} and bˉ\bar{b} is ...

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  13. Question 13

    14 May 2026 S2

    91
    If pˉ,qˉ,rˉ\bar{p}, \bar{q}, \bar{r} are unit vectors such that pˉ×(qˉ×rˉ)=17qˉ\bar{p} \times (\bar{q} \times \bar{r}) = \dfrac{1}{7}\bar{q}, then the angle between pˉ\bar{p} and rˉ\bar{r} is

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