NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions
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Question : 6
Total: 20
Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.
Solution:
Let A(–2, 3, 5), B(1, 2, 3) and C(7, 0, –1) be three given points.
Then AB =√ ( 1 + 2 ) 2 + ( 2 − 3 ) 2 + ( 3 − 5 ) 2 √ 9 + 1 + 4 √ 14
BC =√ ( 7 − 1 ) 2 + ( 0 − 2 ) 2 + ( − 1 − 3 ) 2 √ 36 + 4 + 16 √ 56 2 √ 14
AC =√ ( 7 + 2 ) 2 + ( 0 − 3 ) 2 + ( − 1 − 5 ) 2 √ 81 + 9 + 36 √ 126 3 √ 14
Now AC = AB + BC
Thus, points A, B and C are collinear.
Then AB =
BC =
AC =
Now AC = AB + BC
Thus, points A, B and C are collinear.
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