Question
Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.
Solution
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
∴ lines PQ and PR are parallel.
But P is a common point on both the lines points
∴ P, Q, R are collinear.
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
∴ lines PQ and PR are parallel.
But P is a common point on both the lines points
∴ P, Q, R are collinear.
