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Angle between unit vectors a and b from |a + b| or |a - b|

This type of question, asked 6 times: 20 Apr 2025 S1, 20 Apr 2025 S2, 21 Apr 2025 S1, 15 Apr 2026 S1, 12 May 2026 S2, 13 May 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S1

    132
    If aˉ\bar{a} and bˉ\bar{b} are unit vectors and θ\theta is the angle between them, then a‾+b‾\overline{a}+\overline{b} is a unit vector when θ\theta is

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  2. Question 2

    20 Apr 2025 S2

    112
    If aˉ\bar{a} and bˉ\bar{b} are unit vectors and θ\theta is the angle between them, then tan⁡θ2=\tan\frac{\theta}{2}=

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  3. Question 3

    21 Apr 2025 S1

    115
    If a‾\overline{a} and b‾\overline{b} are unit vectors such that ∣a‾+b‾∣=3|\overline{a}+\overline{b}| =\sqrt{3}, then the angle between a‾\overline{a} and b‾\overline{b} is

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  4. Question 4

    15 Apr 2026 S1

    88
    If aˉ\bar{a} and bˉ\bar{b} are unit vectors and θ (0<θ<π)\theta\ (0 < \theta < \pi) is the angle between them, then the value of ∣aˉ+bˉ∣∣aˉ−bˉ∣\dfrac{|\bar{a} + \bar{b}|}{|\bar{a} - \bar{b}|} is equal to...

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  5. Question 5

    12 May 2026 S2

    90
    If the sum of two unit vectors is a unit vector, then the magnitude of their difference is...

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  6. Question 6

    13 May 2026 S2

    92
    If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| then the angle between a⃗\vec{a} and b⃗\vec{b} is

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