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NCERT Class XI Mathematics - Introduction to Three Dimensional Geometry - Solutions

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Question : 6 of 20
Marks: +1, -0
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\sqrt{(1+2)^2+(2-3)^2+(3-5)^2} = 9+1+4\sqrt{9+1+4} = 14\sqrt{14} units
BC = (7−1)2+(0−2)2+(−1−3)2\sqrt{(7-1)^2+(0-2)^2+(-1-3)^2} = 36+4+16\sqrt{36+4+16} = 56\sqrt{56} = 2142\sqrt{14} units
AC = (7+2)2+(0−3)2+(−1−5)2\sqrt{(7+2)^2+(0-3)^2+(-1-5)^2} = 81+9+36\sqrt{81+9+36} = 126\sqrt{126} = 3143\sqrt{14} units
Now AC = AB + BC
Thus, points A, B and C are collinear.
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