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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 4 of 78
Marks: +1, -0
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 ratios of AB are < (–1 – 2), (–2 –3), (1 – 4) > i.e., < – 3, – 5, –3 >
Direction ratios 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,B and C are collinear.
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