Question:
7. Show that points (4, –3, –1), (5, –7, 6) and (3, 1, –8) are collinear.
Answer:
Given the points are A(4, –3, –1), B(5, –7, 6) and C(3, 1, –8)
Now AB2 = (5 - 4)2 + (-7 + 3)2 + (6 + 1)2 = 1 + 16 + 49 = 66
=> AB = √66 = 8.124
BC2 = (3 - 5)2 + (1 + 7)2 + (-8 - 6)2 = 4 + 64 + 196 = 268
=> BC = √268 = 16.37
CA2 = (4 - 3)2 + (-3 - 1)2 + (-1 + 8)2 = 1 + 16 + 49 = 66
=> CA = √66 = 8.124
Now, AB + BC = 8.124 + 8.124 = 16.25 ≅ CA
So, the points A, B and C are collinear.
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