PYQ Vault
EbooksTutor

Volume of the tetrahedron a plane cuts from the coordinate planes

This type of question, asked 5 times: 11 May 2024 S1, 12 May 2024 S1, 13 May 2024 S2, 18 Apr 2026 S1, 12 May 2026 S2. All 5 questions below, oldest first.

Try each one first, then open its answer.

  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.

    Tap an option to check your answer.

  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

    Tap an option to check your answer.

  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

    Tap an option to check your answer.

  4. Question 4

    18 Apr 2026 S1

    96
    If the plane 2x+3y+z=62x + 3y + z = 6 cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

    Tap an option to check your answer.

  5. Question 5

    12 May 2026 S2

    94
    The volume of the tetrahedron formed by the plane 6x+4y−5z−60=06x + 4y - 5z - 60 = 0 and the coordinate planes is ........... cubic units

    Tap an option to check your answer.