Show that the points (2, 3, 4), (- 1, -2, 1), (5, 8,7) are collinear.

1.	Show that the points (2, 3, 4), (- 1, -2, 1), (5, 8,7) are collinear.
Answer» Let A (2, 3, 4), B (- 1, - 2, 1), C (5, 8, 7) be given Direction ratio of AB are (- 1 - 2), (- 2 - 3) (1 - 4) = (-3,-5,-3) Direction r ratio of AC are (5 - 2), (8 - 3), (7 - 4) = (3, 5,3) The direction ratios of AB and AC are proportional. So AB and AC are parallel But A is common in AB and AC A, B and C are collinear.

Answer»

Let A (2, 3, 4), B (- 1, - 2, 1), C (5, 8, 7) be given

Direction ratio of AB are (- 1 - 2), (- 2 - 3) (1 - 4) = (-3,-5,-3)

Direction r ratio of AC are (5 - 2), (8 - 3), (7 - 4) = (3, 5,3)

The direction ratios of AB and AC are proportional.

So AB and AC are parallel

But A is common in AB and AC

A, B and C are collinear.

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