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Index

Show that 2 Lines are Parallel:

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Show that the line L1 through A(3, -2, 4) and B(5, 1, -2) is parallel to L2 through C(-2, 3, 1) and D(2, 9, -11).

If the lines are parallel, the vectors describing them are proportional.

For L1, the two points give the vector AB = [5 - 3]i + [1 - (-2)]j + [-2 - 4]k = 2i + 3j - 6k

For L2, the two points give CD = [2 - (-2)]i + [9 - 3]j + [-11 - 1]k = 4i + 6j - 12k = 2*AB

Hence the two vectors are proportional and the lines are parallel.