Vektor Segaris dan Sebidang

\begin{equation*}
\begin{split}
\overrightarrow{AB} & = k \:.\: \overrightarrow{BC} \\\\
\overrightarrow{b} - \overrightarrow{a} & = k \:.\: \left[ \: \overrightarrow{c}-\overrightarrow{b} \: \right ] \\\\
\left(\begin{matrix}2\\1\\8\\\end{matrix}\right)-\left(\begin{matrix}8\\x\\5\\\end{matrix}\right) & = k \:.\: \left [ \left( \:\begin{matrix}y\\4\\7\\\end{matrix}\right)-\left(\begin{matrix}2\\1\\8\\\end{matrix}\right) \: \right ]\\\\
\left(\begin{matrix}-6\\1-x\\3\\\end{matrix}\right) & = k \:.\: \left(\begin{matrix}y-2\\3\\-1\\\end{matrix}\right) \\\\
\left(\begin{matrix}-6\\1-x\\3\\\end{matrix}\right) & = \left(\begin{matrix}k(y-2)\\3k\\-k\\\end{matrix}\right)
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
-6 & = k(y - 2) \\\\
-6 & = -3(y - 2) \\\\
-6 & = -3y + 6 \\\\
3y & = 12 \\\\
y & = 4
\end{split}
\end{equation*}