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Point where a line meets a plane

This type of question, asked 6 times: 3 May 2023 S2, 9 May 2024 S2, 11 May 2024 S2, 13 May 2024 S2, 20 Apr 2025 S2, 23 Apr 2025 S1. All 6 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    147
    On which of the following lines lies the point of intersection of the line x−42=y−52=z−31\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1} and the plane x+y+z=2x+y+z=2?

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  2. Question 2

    9 May 2024 S2

    139
    The co-ordinates of the point, where the line x−12=y−2−3=z+54\dfrac{x-1}{2}=\dfrac{y-2}{-3}=\dfrac{z+5}{4} meets the plane 2x+4y−z=32x+4y-z=3, are

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  3. Question 3

    11 May 2024 S2

    106
    If the line x−12=y+13=z−24\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4} meets the plane x+2y+3z=15x+2y+3z=15 at the point P, then the distance of P from the origin is:

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  4. Question 4

    13 May 2024 S2

    117
    The distance of the point (1,6,2)(1,6,2) from the point of intersection of the line x−23=y+14=z−212\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12} and the plane x−y+z=16x-y+z=16 is:

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  5. Question 5

    20 Apr 2025 S2

    131
    The co-ordinates of the point where the line joining the points ( 2,−3,12, - 3,1 ) and ( 3,−4,−53, - 4, - 5 ) and intersects the plane 2x+y+z=72x+y+z= 7 are

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  6. Question 6

    23 Apr 2025 S1

    141
    The distance of the point P(3,4,4)P(3,4,4) from the point of intersection of the line joining the points Q(3,−4,−5),R(2,−3,1)Q(3, - 4, - 5),R(2, - 3,1) and the plane 2x+y+z=72x+y+z= 7 is

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