Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are col… - Vidyadip

Question

Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.

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Answer

Let A(-2, 3, 5), B (1, 2, 3) and C(7, 0, -1) be three given points.
Then $AB = \sqrt {{{(1 + 2)}^2} + {{(2 - 3)}^2} + {{(3 - 5)}^2}}$ $ = \sqrt {9 + 1 + 4} = \sqrt {14}$
$BC = \sqrt {{{(7 - 1)}^2} + {{(0 - 2)}^2} + {{( - 1 - 3)}^2}}$ $= \sqrt {36 + 4 + 16} = \sqrt {56} = 2\sqrt {14}$
$AC = \sqrt {{{(7 + 2)}^2} + {{(0 - 3)}^2} + {{( - 1 - 5)}^2}}$$= \sqrt {81 + 9 + 36} = \sqrt {126} = 3\sqrt {14}$
Now AC = AB + BC

Therefore,A,B,C are collinear.

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