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Maximum of [a b c] when c is a unit vector

This type of question, asked 2 times: 16 Apr 2026 S2, 20 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    16 Apr 2026 S2

    90
    If aˉ=2i^+j^−k^,bˉ=i^+3k^\bar{a} = 2\hat{i} + \hat{j} - \hat{k}, \bar{b} = \hat{i} + 3\hat{k} and cˉ\bar{c} is a unit vector, then the maximum value of the scalar triple product [aˉ bˉ cˉ][\bar{a}\ \bar{b}\ \bar{c}] is

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  2. Question 2

    20 Apr 2026 S2

    89
    If u⃗=i^+2j^−2k^,v⃗=2i^+k^\vec{u} = \hat{i} + 2\hat{j} - 2\hat{k}, \vec{v} = 2\hat{i} + \hat{k} and w⃗\vec{w} is unit vector then the maximum value of scalar triple product [u⃗ v⃗ w⃗][\vec{u}\,\vec{v}\,\vec{w}] is

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