Question:
(b) Show that the points \( A(2,3,4) \), \( B(-1,-2,1) \), and \( C(5,8,7) \) are collinear.
(b) Show that the points \( A(2,3,4) \), \( B(-1,-2,1) \), and \( C(5,8,7) \) are collinear.
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To check collinearity, verify if vectors are scalar multiples of each other.
Updated On: Mar 1, 2025
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Solution and Explanation
Findvectors\(\overrightarrow{AB}\)and\(\overrightarrow{BC}\):
\[
\overrightarrow{AB}=(-1-2,-2-3,1-4)=(-3,-5,-3).
\]
\[
\overrightarrow{BC}=(5-(-1),8-(-2),7-1)=(6,10,6).
\]
Checkif\(\overrightarrow{AB}\)and\(\overrightarrow{BC}\)arescalarmultiples:
\[
\frac{-3}{6}=\frac{-5}{10}=\frac{-3}{6}=-\frac{1}{2}.
\]
Sincetheratiosareequal,thepointsarecollinear.
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