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Perpendicular distance of a point from a line

This type of question, asked 8 times: 9 May 2023 S1, 9 May 2024 S1, 12 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S1, 17 Apr 2026 S2, 12 May 2026 S2, 19 May 2026 S1. All 8 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    145
    The length of the perpendicular from the point A(1,−2,−3)A(1,-2,-3) on the line x−12=y+3−1=z+1−2\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z+1}{-2} is

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  2. Question 2

    9 May 2024 S1

    104
    The distance of the point having position vector i^−2j^−6k^\hat{i}-2\hat{j}-6\hat{k}, from the straight line passing through the point (2,−3,−4)(2,-3,-4) and parallel to the vector 6i^+3j^−4k^6\hat{i}+3\hat{j}-4\hat{k} is

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  3. Question 3

    12 May 2024 S1

    136
    The distance of the point P(−2,4,−5)P(-2,4,-5) from the line x+33=y−45=z+86\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6} is

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  4. Question 4

    14 May 2024 S2

    113
    The length of the perpendicular drawn from the point (1,2,3)(1,2,3) to the line x−63=y−72=z−7−2\frac{x-6}{3} = \frac{y-7}{2} = \frac{z-7}{-2} is

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  5. Question 5

    19 Apr 2025 S1

    104
    The distance of the point (−3,2,3)( - 3,2,3) from the line passing through (4,6,−2)(4,6, - 2) and having direction ratios −1,2,3- 1,2,3 is ____\_\_\_\_ units.

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  6. Question 6

    17 Apr 2026 S2

    96
    If the distance of point B(2,1,−3)B(2, 1, -3) from the line passing through the point A(4,−2,2)A(4, -2, 2), and parallel to the vector c⃗=−4i^−6j^−2k^\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k} is xx, then x4+x2+541=x^4 + x^2 + 541 =

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  7. Question 7

    12 May 2026 S2

    92
    The length of the perpendicular from the point (3,2,1)(3, 2, 1) to the line x−7−2=y−72=z−63\dfrac{x - 7}{-2} = \dfrac{y - 7}{2} = \dfrac{z - 6}{3} is kk units. then the value of kk....

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  8. Question 8

    19 May 2026 S1

    96
    The distance of the point (1,1,1)(1, 1, 1) from the line passing through the point (2,3,4)(2, 3, 4) whose direction ratios are 2,−3,62, -3, 6 is:

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