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Plane through the line of intersection of 2x - y + z = 3 and 4x - 3y + 5z = -9, parallel to a given line

The same question, asked 2 times: 20 Apr 2025 S2, 13 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    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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  2. Question 2

    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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