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Perpendicular distance of a point from a line

This type of question, asked 4 times: 25 Jan 2023, 22 Jan 2025, 21 Jan 2026 S2, 5 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    25 Jan 2023

    77
    The distance of the point P(4,6,−2)P(4,6, - 2) from the line passing through the point (−3,2,3)( - 3,2,3) and parallel to a line with direction ratios 3,3,−13,3, - 1 is equal to:

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  2. Question 2

    22 Jan 2025

    134
    The perpendicular distance, of the line x−12=y+2−1=z+32\frac{x - 1}{2}=\frac{y + 2}{- 1}=\frac{z + 3}{2} from the point P(2,−10,1)P(2, - 10,1), is:

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  3. Question 3

    21 Jan 2026 S2

    57
    Let the line L pass through the point (−3,5,2)( - 3,5,2) and make equal angles with the positive coordinate axes. If the distance of L from the point ( −2,r,1- 2,r,1 ) is 143\sqrt{\frac{14}{3}}, then the sum of all possible values of rr is :

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  4. Question 4

    5 Apr 2026 S1

    63
    The square of the distance of the point P(5,6,7)P(5,6,7) from the line x−22=y−53=z−24\frac{x- 2}{2}=\frac{y- 5}{3}=\frac{z- 2}{4} is equal to :

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