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Plane rotated through a right angle about its line of intersection with another plane

The same question, asked 2 times: 26 Jun 2022*, 12 Apr 2023. Every wording below, oldest first.

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  1. Question 1

    26 Jun 2022

    164
    If the plane 2x+y−5z=02x + y - 5z = 0 is rotated about its line of intersection with the plane 3x−y+4z−7=03x - y + 4z - 7 = 0 by an angle of π2\frac{\pi}{2}, then the plane after the rotation passes through the point :

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  2. Question 2

    12 Apr 2023

    75
    Let the plane P:4x−y+z=10P:4x-y+z=10 be rotated by an angle π2\frac{\pi}{2} about its line of intersection with the plane x+y−z=4x+y-z=4. If α\alpha is the distance of the point (2,3,−4)(2,3,-4) from the new position of the plane PP, then 35α35\alpha is

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