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Consider the lines L1 and L2 given by L1 : (x - 1)/2 = (y - 3)/1 = (z - 2)/2 L2 : (x - 2)/1 = (y - 2)/2 = (z - 3)/3 A line L3 having direction ratios 1, -1, -2, intersects L1 and L2 at the points P and Q respectively. Then the length of line segment PQ is

1. 3√2
2. 2√6
3. 4√3
4. 4

Correct answer: 2√6

Solution

The length of the line segment PQ is determined by the distance between the intersection points of line L3 with lines L1 and L2. By calculating the coordinates of these intersection points using the direction ratios and the equations of L1 and L2, we find that the distance between them is 2√6.

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