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JEE Main 2024 Mathematics question

MathematicsThree Dimensional GeometryJEE Main 2024

A line passes through A(4, −6, −2) and B(16, −2, 4). The point P(a, b, c), where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, −12, 3) is equal to .

Answer: 22

Solution

The direction ratios of AB are (12, 4, 6) ∝ (6, 2, 3), with |d| = 7. The point at distance 21 from A is (4 + 21 × 6/7, −6 + 21 × 2/7,

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Question ID VK-017281