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Feet of the perpendiculars from one point to two lines

This type of question, asked 2 times: 31 Jan 2024, 7 Apr 2025. All 2 questions below, oldest first.

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  1. Question 1

    31 Jan 2024

    84
    Let QQ and RR be the feet of perpendiculars from the point P(a,a,a)P(a,a,a) on the lines x=y,z=1x = y,z = 1 and x=−yx = - y, z=−1z = - 1 respectively. If ∠QPR\angle QPR is a right angle, then 12a212a^{2} is equal to

  2. Question 2

    7 Apr 2025

    141
    Consider the lines L1:x−1=y−2=zL_{1}:x- 1 =y- 2 =z and L2:x−2=y=z−1L_{2}:x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5,1,−3)P(5,1, - 3) on the lines L1L_{1} and L2L_{2} be QQ and RR respectively. If the area of the triangle PQRPQR is AA, then 4A24A^{2} is equal to :

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