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Projection of the segment joining two points on a line

This type of question, asked 4 times: May 2021 S1, 10 May 2023 S2, 10 May 2024 S1, 22 Apr 2025 S2. All 5 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    132
    What will be the projection of the vector 4i^−3j^+k^4\hat{i} - 3\hat{j} + \hat{k} on the line joining the points (2,3,−1)(2,3,-1) and (−2,−4,3)(-2,-4,3)?

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  2. Question 2

    10 May 2023 S2

    133
    The projection of AB→\overrightarrow{AB} on CD→\overrightarrow{CD}, where A≡(2,−3,0)A\equiv(2,-3,0), B≡(1,−4,−2)B\equiv(1,-4,-2), C≡(4,6,8)C\equiv(4,6,8) and D≡(7,0,10)D\equiv(7,0,10) is

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  3. Question 3

    10 May 2024 S1

    142
    Vector projection of AB→\overrightarrow{AB} on CD→\overrightarrow{CD}, A(2,-3,0), B(1,-4,-2), C(4,6,8), D(7,0,10)

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  4. Question 4

    10 May 2024 S1

    149
    Scalar projection of segment AB on line with d.r.s 6,-2,3. A(-2,0,3), B(1,4,2).

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  5. Question 5

    22 Apr 2025 S2

    150
    The projection of the line segment joining P(2,−1,0)P(2, - 1,0) and Q(3,2,−1)Q(3,2, - 1) on the line whose direction ratios are 1,2,21,2,2 is

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