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Bound on a sum of squared lengths using |a + b + c|^2 >= 0

This type of question, asked 2 times: 19 Apr 2025 S2, 18 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S2

    138
    If a‾,b‾,c‾\overline{a},\overline{b},\overline{c} are three vectors such that a‾∣=3\overline{a}\mid = 3, ∣b‾∣=5,∣c‾∣=7|\overline{b}| = 5,|\overline{c}| = 7 then ∣a‾−b‾∣2+∣b‾−c‾∣2+∣c‾−a‾∣2|\overline{a}-\overline{b}|^{2}+ |\overline{b}-\overline{c}|^{2}+ |\overline{c}-\overline{a}|^{2} does not exceed

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  2. Question 2

    18 Apr 2026 S1

    90
    Let aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} be three vectors of equal magnitude such that the angle between aˉ\bar{a} and bˉ\bar{b} is α\alpha, bˉ\bar{b} and cˉ\bar{c} is β\beta, cˉ\bar{c} and aˉ\bar{a} is γ\gamma. Then the minimum value of cos⁡α+cos⁡β+cos⁡γ\cos\alpha + \cos\beta + \cos\gamma is ...

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