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Two points on a line at the same given distance from a point: area of the triangle they form

The same question, asked 2 times: 28 Jun 2022*, 26 Jul 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    28 Jun 2022

    75
    If two distinct points Q,RQ,R lie on the line of intersection of the planes −x+2y−z=0-x + 2y - z = 0 and 3x−5y+2z=03x - 5y + 2z = 0 and PQ=PR=18PQ = PR =\sqrt{18} where the point PP is (1,−2,3)(1, - 2,3), then the area of the triangle PQRPQR is equal to

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  2. Question 2

    26 Jul 2022

    90
    Let QQ and RR be two points on the line x+12=y+23=z−12\frac{x + 1}{2}=\frac{y + 2}{3}=\frac{z - 1}{2} at a distance 26\sqrt{26} from the point P(4,2,7)P(4,2,7). Then the square of the area of the triangle PQRPQR is