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Two lines in 3D space are given as: L1: r = (-i + 3k) + lambda*(2i - p*j) and L2: r = (-j + 2k) + mu*(i - j + 2k). If the shortest distance between L1 and L2 equals 3/sqrt(21), find the sum of all possible values of p.
- 3
- 4
- 5
- 6
Correct answer: 5
Solution
Apply the standard shortest-distance formula for skew lines. Computing the cross product of the direction vectors and dotting with the displacement vector between the two known points gives an equation in p; solving yields two values whose sum is required.
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