The points (2, 3, 4),(-1, -2, 1),and (5, 8, 7 | vedclass

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(A) Let the points be $A(2, 3, 4)$,$B(-1, -2, 1)$,and $C(5, 8, 7)$.We check if the points are collinear by calculating the distance between them.$AB =

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collinear

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(A) Let the points be $A(2, 3, 4)$,$B(-1, -2, 1)$,and $C(5, 8, 7)$.We check if the points are collinear by calculating the distance between them.$AB = \sqrt{(-1-2)^2 + (-2-3)^2 + (1-4)^2} = \sqrt{(-3)^2 + (-5)^2 + (-3)^2} = \sqrt{9 + 25 + 9} = \sqrt{43}$.$BC = \sqrt{(5-(-1))^2 + (8-(-2))^2 + (7-1)^2} = \sqrt{6^2 + 10^2 + 6^2} = \sqrt{36 + 100 + 36} = \sqrt{172} = 2\sqrt{43}$.$AC = \sqrt{(5-2)^2 + (8-3)^2 + (7-4)^2} = \sqrt{3^2 + 5^2 + 3^2} = \sqrt{9 + 25 + 9} = \sqrt{43}$.Since $AB + AC = \sqrt{43} + \sqrt{43} = 2\sqrt{43} = BC$,the points $A, B, C$ are collinear.

The points $(2, 3, 4)$,$(-1, -2, 1)$,and $(5, 8, 7)$ are

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