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Plane through (1,1,1) parallel to lines with direction ratios 1, 0, -1 and -1, 1, 0: volume of tetrahedron OABC

The same question, asked 3 times: 11 May 2024 S1*, 12 May 2024 S1*, 13 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2024 S1

    120
    A plane is parallel to two lines, whose direction ratios are (1,0,−1)(1,0,-1) and (−1,1,0)(-1,1,0) and it contains the point (1,1,1)(1,1,1). If it cuts coordinate axes (X, Y, Z axes resp.) at A, B, C, then the volume of the tetrahedron OABC is cu. Units.

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  2. Question 2

    12 May 2024 S1

    122
    A plane is parallel to two lines whose direction ratios are 1,0,−11,0,-1 and −1,1,0-1,1,0 and it contains the point (1,1,1)(1,1,1). If it cuts the co-ordinate axes at A,B,CA,B,C, then the volume of the tetrahedron OABC (in cubic units) is

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  3. Question 3

    13 May 2024 S2

    138
    A plane is parallel to two lines whose direction ratios are 2,0,−22,0,-2 and −2,2,0-2,2,0 and it contains the point (2,2,2)(2,2,2). If it cuts co-ordinate axes at A, B, C, then the volume of the tetrahedron OABC (in cubic units) is

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