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Line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2 makes angle a with the x-axis: find cos a or sec a

The same question, asked 2 times: 9 May 2023 S2, 9 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    9 May 2023 S2

    140
    Let L be the line of intersection of the planes 2x+3y+z=12x+3y+z=1 and x+3y+2z=2x+3y+2z=2. If L makes an angle α\alpha with the positive X-axis, then cos⁡α\cos\alpha equals

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  2. Question 2

    9 May 2024 S2

    113
    If a line LL is the line of intersection of the planes 2x+3y+z=12x + 3y + z = 1 and x+3y+2z=2x + 3y + 2z = 2. If line LL makes an angle α\alpha with the positive X-axis, then the value of sec⁡α\sec\alpha is

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