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Show that the points A(5, 4, 2), B(6, 2,...

Show that the points A(5, 4, 2), B(6, 2, -1) and C(8, -2, -7) are collinear.

Text Solution

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A(5, 4, 2), B(6, 2, -1) and C(8, -2, -7) are given points
`AB = sqrt((6-5)^(2)+(2-4)^(2)+(-1-2)^(2) )=sqrt(14)` units
`BC = sqrt((8-6)^(2)+(-2-2)^(2)+(-7+1)^(2))=2sqrt(14)` units
and `AC = sqrt((8-5)^(2) + (-2-4)^(4)+(-7-2)^(2))=3sqrt(14)` units
Now `sqrt(14)+2sqrt(14) = 3sqrt(14)`
`rArr AB+ BC= AC`
Hence, the given points are collinear.
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