Let \(P\) be a plane \(l x+m y+n z=0\) containing the line, \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\). If plane \(P\…

Let \(P\) be a plane \(l x+m y+n z=0\) containing the line, \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\). If plane \(P\) divides the line segment \(A B\) joining points \(A(-3,-6,1)\) and \(B(2,4,-3)\) in ratio \(k: 1\), then the value of \(k\) is equal to:

[JEE Main 2021, 16 Mar (Shift 1)]