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Plane through the line of intersection of two planes satisfying one more condition

This type of question, asked 9 times: 15 May 2023 S2, 16 May 2023 S1, 9 May 2024 S2, 10 May 2024 S2, 19 Apr 2025 S2, 20 Apr 2025 S2, 26 Apr 2025 S2, 13 Apr 2026 S2, 19 May 2026 S2. All 9 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    128
    The vector equation of the plane through the line of intersection of the planes x+y+z=1x+y+z=1 and 2x+3y+4z=52x+3y+4z=5, which is perpendicular to the plane x−y+z=0x-y+z=0, is

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  2. Question 2

    16 May 2023 S1

    113
    The equation of the plane, passing through the intersection of the planes x+y+z=1x+y+z=1 and 2x+3y−z+4=02x+3y-z+4=0 and parallel to Y-axis is

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  3. Question 3

    9 May 2024 S2

    147
    The equation of a plane, containing the line of intersection of the planes 2x−y−4=02x-y-4=0 and y+2z−4=0y+2z-4=0 and passing through the point (2,1,0)(2,1,0), is

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  4. Question 4

    10 May 2024 S2

    128
    The plane through the intersection of planes x+y+z=1x+y+z=1 and 2x+3y−z+4=02x+3y-z+4=0 and parallel to Y-axis also passes through the point

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  5. Question 5

    19 Apr 2025 S2

    130
    The equation of the plane passing through the line of intersection of the planes x+y+z=1x+y+z= 1 and 3x+4y+5z=23x+ 4y+ 5z= 2 and perpendicular to the XY - plane is

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  6. Question 6

    20 Apr 2025 S2

    108
    The equation of the plane passing through the point of intersection of the planes 2x−y+z−3=02x-y+z- 3 = 0 and 4x−3y+5z+9=04x- 3y+ 5z+ 9 = 0 and parallel to the line x+12=y+34=z−35\frac{x+ 1}{2}=\frac{y+ 3}{4}=\frac{z- 3}{5} is αx+βy+γz+d=0\alpha x+\beta y+\gamma z+d= 0 Then α+β+γ+d=\alpha+\beta+\gamma+d=

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  7. Question 7

    26 Apr 2025 S2

    145
    The equation of the plane passing through the point ( 1,1,11,1,1 ) and through the line of intersection of x+2y−z+1=0x+ 2y-z+ 1 = 0 and 3x−y−4z+3=03x-y- 4z+ 3 = 0 is

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  8. Question 8

    13 Apr 2026 S2

    95
    The equation of the plane passing through the intersection of planes 2x−y+z=32x - y + z = 3, 4x−3y+5z=−94x - 3y + 5z = -9 and parallel to the line x+12=y+34=z−35\dfrac{x + 1}{2} = \dfrac{y + 3}{4} = \dfrac{z - 3}{5} is...

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  9. Question 9

    19 May 2026 S2

    96
    The equation of a plane passing through the intersection of two planes r⃗⋅(i^−2j^+3k^)=4\vec{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 4 and r⃗⋅(2i^+j^−3k^)=7\vec{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = 7 and parallel to Y-axis is

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