Given the points A(5,1,3), B(7,9,-1) , C(1, -15, 11) how do I determine if they are or not on a straight line?
Hello, Craka!
Another method . . .
Given the points: .$\displaystyle A(5,1,3),\;B(7,9,\text{-}1),\;C(1, \text{-}15, 11)$
how do I determine if they are or not on a straight line?
Find vector $\displaystyle \overrightarrow{AB}\!:\;\;\overrightarrow{AB} \:=\:\langle 7-5,\:9-1,\:\text{-}1-3\rangle \:=\:\langle 2,\:8,\:\text{-}4\rangle \;=\;2\langle 1,\:4,\:\text{-}2\rangle $
Find vector $\displaystyle \overrightarrow{BC}\!:\;\;\overrightarrow{BC} \:=\:\langle 1-7,\:\text{-}15-9,\:11-(\text{-}1)\rangle \:=\:\langle \text{-}6,\:\text{-}24,\:12\rangle \:=\: -6\langle1,\:4,\:\text{-}2\rangle
$
Since $\displaystyle \overrightarrow{AB} \parallel \overrightarrow{BC},\;\;A,B,C \text{ are collinear.}$