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Question
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
Solution
Let A = (2, 3, 4), B = (-1, -2, 1) and C = (5, 8, 7)
Direction ratio of AB are < (-1 - 2), (- 2 - 3), (1 - 4) >
⇒ i.e., < -3, -5, -3 >
Direction ratio of AC are < (5 - 2), (8 - 3), (7 - 4) >
⇒ i.e., < 3, 5, 3 >
It is clear that the direction ratios of AB and AC are proportional.
Hence, AB and AC are parallel, but these have a point A in common.
Therefore A, Band Care collinear.
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