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Ratio in which a point or a coordinate plane divides a segment

This type of question, asked 2 times: 12 May 2026 S2, 13 May 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    12 May 2026 S2

    96
    The ratio in which the point i^+2j^+3k^\hat{i} + 2\hat{j} + 3\hat{k} divides the line segment joining −2i^+3j^+5k^-2\hat{i} + 3\hat{j} + 5\hat{k} and 7i^−k^7\hat{i} - \hat{k} is....

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  2. Question 2

    13 May 2026 S1

    96
    The ratio and the coordinates of the point where the segment joining (3,5,6)(3, 5, 6) and (4,6,−3)(4, 6, -3) is divided by the YZ-plane are respectively:

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