Show that the line segment joining the points A(1, 2, 3) and B (4, 5, 7) is parallel to the segment joining the points C(-4, 3, -6) and D (2, 9, 2).

Given A(1, 2, 3), B(4, 5, 7), the line joining these two points will be


AB = 3i + 3j + 4k


And the line segment joining, C(-4, 3, -6) and D(2, 9, 2) will be


CD = 6i + 6j + 8k


If CD = r(AB), where r is a scalar constant then,


The two lines are parallel.


Here, CD = 2(AB),


Thus, the two lines are parallel.


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