Question

(b) Show that the points \( A(2,3,4) \), \( B(-1,-2,1) \), and \( C(5,8,7) \) are collinear.

Hint:

To check collinearity, verify if vectors are scalar multiples of each other.

Answer 1

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.