Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collin… - Vidyadip

Question

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

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Answer

Let P(2, 3, 4), Q(-1, -2, 1), R(5, 8, 7) be given points.
The direction ratios of PQ are -1 - 2, -2 - 3, 1 - 4 i.e. -3, -5, -3
The direction ratios of PR are 5 - 2, 8 - 3, 7 - 4 i.e. 3, 5, 3
Since $\frac{-3}{3}=\frac{-5}{5}=\frac{-3}{3}$
$\therefore$ lines PQ and PR are parallel.
But P is a common point on both the lines points
$\therefore$ P, Q, R are collinear.

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