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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 64 of 78
Marks: +1, -0
If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (– 4, 3, – 6) and (2, 9, 2) respectively, then find the angle between the line AB and CD.
Solution:  
Direction ratios of AB are
< 4 – 1, 5 – 2, 7 – 3 > i.e. < 3, 3, 4 > ...(1)
Direction ratios of CD are
<2 – (–4), 9 – 3, 2 – (–6) > i.e. < 6, 6, 8 > ...(2)
From (1) and (2), Direction ratios of AB and CD are proportional ⇒ The lines AB and CD are parallel.
Hence the angle between AB and CD is 0°.
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