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Volume of a tetrahedron is given: find the unknown coordinate

This type of question, asked 3 times: 12 May 2024 S2, 21 Apr 2025 S2, 20 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    12 May 2024 S2

    135
    If the volume of tetrahedron, whose vertices are A(1,2,3), B(−3,−1,1), C(2,1,3)A(1,2,3),\, B(-3,-1,1),\, C(2,1,3) and D(−1,2,x)D(-1,2,x) is 116\frac{11}{6} cubic units, then the value of xx is

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  2. Question 2

    21 Apr 2025 S2

    125
    The volume of the tetrahedron whose coterminous edges are represented by a‾=−12i^+pk^,b‾=3j^,−k^,c‾=2i^+j^−15k^\overline{a}= - 12\widehat{i}+ p\widehat{k},\overline{b}= 3\widehat{j}, -\widehat{k},\overline{c}= 2\widehat{i}+\widehat{j}- 15\widehat{k} is 570 cu. units, then p=p =

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  3. Question 3

    20 Apr 2026 S1

    89
    The volume of the tetrahedron whose vertices are A(−1,2,3),B(3,−2,1),C(p,1,3),D(−1,−2,4)\mathrm{A}(-1, 2, 3), \mathrm{B}(3, -2, 1), \mathrm{C}(p, 1, 3), \mathrm{D}(-1, -2, 4) is 163\dfrac{16}{3} cubic units then the value of p is

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