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Tetrahedron with vertices (1, -6, 10), (-1, -3, 7), (5, -1, k), (7, -4, 7) has volume 11: find k

The same question, asked 3 times: 11 May 2023 S1, 10 May 2024 S2, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    11 May 2023 S1

    141
    If the volume of tetrahedron whose vertices are A≡(1,−6,10)A\equiv(1,-6,10), B≡(−1,−3,7)B\equiv(-1,-3,7), C≡(5,−1,k)C\equiv(5,-1,k) and D≡(7,−4,7)D\equiv(7,-4,7) is 11 cu. units, then the value of k is

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  2. Question 2

    10 May 2024 S2

    101
    If the volume of tetrahedron, whose vertices are with position vectors i^−6j^+10k^, −i^−3j^+7k^\hat{i}-6\hat{j}+10\hat{k},\,-\hat{i}-3\hat{j}+7\hat{k}, 5i^−j^+λk^5\hat{i}-\hat{j}+\lambda\hat{k} and 7i^−4j^+7k^7\hat{i}-4\hat{j}+7\hat{k} is 11 cubic units, then value of λ\lambda is

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  3. Question 3

    13 Apr 2026 S1

    87
    The volume of a tetrahedron with vertices 5i^−j^+k^,7i^−4j^+pk^,i^−6j^+10k^5\hat{i} - \hat{j} + \hat{k}, 7\hat{i} - 4\hat{j} + p\hat{k}, \hat{i} - 6\hat{j} + 10\hat{k} and −i^−3j^+7k^-\hat{i} - 3\hat{j} + 7\hat{k} is 11 cubic units, then one of the values of p is

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