The points (-2, 4, 7),(3, -6, -8),and (1, -2, | vedclass

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Question

(A) Let the points be $A(-2, 4, 7)$,$B(3, -6, -8)$,and $C(1, -2, -2)$.To check if the points are collinear,we calculate the direction ratios of lines

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Collinear

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(A) Let the points be $A(-2, 4, 7)$,$B(3, -6, -8)$,and $C(1, -2, -2)$.To check if the points are collinear,we calculate the direction ratios of lines $AB$ and $BC$.The direction ratios of line $AB$ are $(3 - (-2), -6 - 4, -8 - 7) = (5, -10, -15)$.The direction ratios of line $BC$ are $(1 - 3, -2 - (-6), -2 - (-8)) = (-2, 4, 6)$.We observe that the ratio of the direction ratios is $\frac{5}{-2} = \frac{-10}{4} = \frac{-15}{6} = -2.5$.Since the direction ratios are proportional,the lines $AB$ and $BC$ are parallel.Because they share a common point $B$,the points $A, B$,and $C$ must be collinear.

The points $(-2, 4, 7)$,$(3, -6, -8)$,and $(1, -2, -2)$ are:

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