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Value of m making the volume of the parallelepiped on i + mj + k, j + mk, mi + k minimum

The same question, asked 4 times: 2 May 2023 S1, 4 May 2023 S1, 10 May 2024 S2, 19 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    113
    The volume of parallelopiped formed by vectors i^+mj^+k^\hat{i} + m\hat{j} + \hat{k}, j^+mk^\hat{j} + m\hat{k} and mi^+k^m\hat{i} + \hat{k} becomes minimum when mm is

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  2. Question 2

    4 May 2023 S1

    120
    The value of aa for which the volume of parallelepiped formed by i^+aj^+k^\hat{i}+a\hat{j}+\hat{k}, j^+ak^\hat{j}+a\hat{k} and ai^+k^a\hat{i}+\hat{k} becomes minimum is

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  3. Question 3

    10 May 2024 S2

    116
    The value of aa, so that the volume of parallelepiped formed by i^+aj^+k^\hat{i}+a\hat{j}+\hat{k}, j^+ak^\hat{j}+a\hat{k} and ai^+k^a\hat{i}+\hat{k} becomes minimum, is

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  4. Question 4

    19 Apr 2026 S1

    90
    The value of xx so that the volume of the parallelopiped formed by the vectors i^+xj^+k^\hat{i} + x\hat{j} + \hat{k}, j^+xk^\hat{j} + x\hat{k} and xi^+k^x\hat{i} + \hat{k} is minimum, is

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