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Plane through a point whose normal has given direction angles

This type of question, asked 2 times: 9 May 2024 S1, 12 May 2024 S1. All 2 questions below, oldest first.

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  1. Question 1

    9 May 2024 S1

    112
    A vector n⃗\vec{n} is inclined to X-axis at 45∘45^\circ, Y-axis at 60∘60^\circ and at an acute angle to Z-axis. If n⃗\vec{n} is normal to a plane passing through the point (−2,1,1)(-\sqrt{2},1,1), then equation of the plane is

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  2. Question 2

    12 May 2024 S1

    126
    The equation of the plane through (−1,1,2)(-1,1,2) whose normal makes equal acute angles with coordinate axes is

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