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Distance of a point from a plane measured parallel to a given line

This type of question, asked 7 times: 2021 Paper 6, 2021 Paper 20, 29 Jul 2022, 24 Jan 2023, 11 Apr 2023, 13 Apr 2023, 15 Apr 2023. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 6

    81
    If the distance of the point (1,−2,3)(1, - 2,3) from the plane x+2y−3z+10=0x+ 2y- 3z+ 10 = 0 measured parallel to the line, x−13=2−ym=z+31\frac{x- 1}{3}=\frac{2 -y}{m}=\frac{z+ 3}{1} is 72\sqrt{\frac{7}{2}}, then the value of ∣m∣|m| is equal to

  2. Question 2

    2021 Paper 20

    66
    The distance of the point (1,−2,3)(1, - 2,3) from the plane x−y+z=5x - y + z = 5 measured parallel to a line, whose direction ratios are 2,3,−62,3, - 6 is:

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  3. Question 3

    29 Jul 2022

    69
    If the foot of the perpendicular from the point A(−1,4,3)A( - 1,4,3) on the plane P:2x+my+nz=4P:2x + my + nz = 4, is (−2,72,32)\left( - 2,\frac{7}{2},\frac{3}{2} \right), then the distance of the point A from the plane PP, measured parallel to a line with direction ratios 3,−1,−43, - 1, - 4, is equal to:

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  4. Question 4

    24 Jan 2023

    76
    The distance of the point (−1,9,−16)( - 1,9, - 16) from the plane 2x+3y−z=52x + 3y - z = 5 measured parallel to the line x+43=2−y4=z−312\frac{x + 4}{3}=\frac{2 - y}{4}=\frac{z - 3}{12} is

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  5. Question 5

    11 Apr 2023

    152
    Let the line passing through the points, P(2,−1,2)P(2, - 1,2) and Q(5,3,4)Q(5,3,4) meet the plane x−y+z=4x - y + z = 4 at the point RR. Then the distance of the point RR from the plane x+2y+3z+2=0x + 2y + 3z + 2 = 0 measured parallel to the line x−72=y+32=z−21\frac{x - 7}{2}=\frac{y + 3}{2}=\frac{z - 2}{1} is equal to

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  6. Question 6

    13 Apr 2023

    65
    The distance of the point (−1,2,3)( - 1,2,3) from the plane r→⋅(i^−2j^+3k^)=10\overrightarrow{r}\cdot (\widehat{i}- 2\widehat{j}+ 3\widehat{k}) = 10 parallel to the line of the shortest distance between the lines r→=(i^−j^)+λ(2i^+k^)\overrightarrow{r}= (\widehat{i}-\widehat{j}) + \lambda(2\widehat{i}+\widehat{k}) and r→=(2i^−j^)+μ(i^−j^+k^)\overrightarrow{r}= (2\widehat{i}-\widehat{j}) + \mu(\widehat{i}-\widehat{j}+\widehat{k}) is :

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  7. Question 7

    15 Apr 2023

    83
    Let the plane PP contain the line 2x+y−z−3=0=5x−3y+4z+92x + y - z - 3 = 0 = 5x - 3y + 4z + 9 and be parallel to the line x+22=3−y−4=z−75\frac{x + 2}{2}=\frac{3 - y}{- 4}=\frac{z - 7}{5}. Then the distance of the point A(8,−1,−19)A(8, - 1, - 19) from the plane P measured parallel to the line x−3=y−54=2−z−12\frac{x}{- 3}=\frac{y - 5}{4}=\frac{2 - z}{- 12} is equal to