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

This type of question, asked 2 times: 26 Jun 2022, 12 Apr 2023. All 3 questions 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

    26 Jun 2022

    75
    Let the plane 2x+3y+z+20=02x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x−3y+5z=8x - 3y + 5z = 8. If the mirror image of the point (2,−12,2)\left( 2, -\frac{1}{2},2 \right) in the rotated plane is B(a,b,c)B(a,b,c), then :

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  3. Question 3

    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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