Correct option is (3) 75
\(\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}=\lambda \quad ....(1)\)
\(\mathrm{x}=3 \lambda-6, \mathrm{y}=2 \lambda, \mathrm{z}=\lambda-1\)
\(\frac{x-7}{4}=\frac{y-9}{3}=\frac{z-4}{2}=\mu \quad....(2)\)
\(\mathrm{x}=4 \mu+7, \mathrm{y}=3 \mu+9, \mathrm{z}=2 \mu+4\)
\(3 \lambda-6=4 \mu+7 \Rightarrow 3 \lambda-4 \mu=13 \quad....(3) \times 2\)
\(2 \lambda=3 \mu+9 \Rightarrow 2 \lambda-3 \mu=9 \quad....(4) \times 3\)
\(\begin{array} {l}6 \lambda-8 \mu=26\\ 6 \lambda-9 \mu=27\\ -\quad+\quad-\\\hline\quad\mu=-1 \end{array}\)
\(\Rightarrow 3 \lambda-4(-1)=13\)
\(3 \lambda=9\)
\(\lambda=3\)
int. point \((3,6,2) ;(7,8,9)\)
\(\mathrm{d}^{2}=16+4+49=69\)
\(\mathrm{d}^{2}+6=69+6=75\)
