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Show that the Points (2, 3, 4), (−1, −2, 1), (5, 8, 7) Are Collinear. - CBSE (Science) Class 12 - Mathematics

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Question

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

Solution

The given points are A (2, 3, 4), B (− 1, − 2, 1), and C (5, 8, 7).

It is known that the direction ratios of line joining the points, (x1y1z1) and (x2y2z2), are given by, x2 − x1y2 − y1, and z2 − z1.

The direction ratios of AB are (−1 − 2), (−2 − 3), and (1 − 4) i.e., −3, −5, and −3.

The direction ratios of BC are (5 − (− 1)), (8 − (− 2)), and (7 − 1) i.e., 6, 10, and 6.

It can be seen that the direction ratios of BC are −2 times that of AB i.e., they are proportional.

Therefore, AB is parallel to BC. Since point B is common to both AB and BC, points A, B, and C are collinear.

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 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 11: Three Dimensional Geometry
Q: 4 | Page no. 467
Solution Show that the Points (2, 3, 4), (−1, −2, 1), (5, 8, 7) Are Collinear. Concept: Direction Cosines and Direction Ratios of a Line.
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