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Perpendicular lines given in non-standard form: find the unknown

This type of question, asked 2 times: 26 Jun 2022, 5 Apr 2024. All 2 questions below, oldest first.

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  1. Question 1

    26 Jun 2022

    74
    If the two lines l1:x−23=y+1−2,z=2l_{1}:\frac{x - 2}{3}=\frac{y + 1}{- 2},z = 2 and l2:x−11=2y+3α=z+52l_{2}:\frac{x - 1}{1}=\frac{2y + 3}{\alpha}=\frac{z + 5}{2} are perpendicular, then an angle between the lines l2l_{2} and l3:1−x3=2y−1−4=z4l_{3}:\frac{1 - x}{3}=\frac{2y - 1}{- 4}=\frac{z}{4} is :

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  2. Question 2

    5 Apr 2024

    80
    If the line 2−x3=3y−24λ+1=4−z\frac{2 - x}{3}=\frac{3y - 2}{4\lambda + 1}= 4 - z makes a right angle with the line x+33μ=1−2y6=5−z7\frac{x + 3}{3\mu}=\frac{1 - 2y}{6}=\frac{5 - z}{7}, then 4λ+9μ4\lambda + 9\mu is equal to :

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