If
\[
\vec{OA}=\hat i-6\hat j+9\hat k,\qquad
\vec{OB}=\hat i+3\hat j+5\hat k,
\qquad
\vec{OC}=2\hat i+\beta\hat j+7\hat k
\]
are the position vectors of three collinear points \(A,B,C\), then the ratio in which \(B\) divides \(AC\) is
Show Hint
For collinear points, if
\[
\overrightarrow{AB}=k\overrightarrow{BC}
\]
with \(k<0\), the point \(B\) divides the line externally. The absolute value of \(k\) gives the ratio.