Mathematics - Vector Question with Solution | TestHub

$\begin{array}{rl}& \frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}=\lambda ....(1)\\ & x=3\lambda -6,y=2\lambda ,z=\lambda -1\\ & \frac{x-7}{4}=\frac{y-9}{3}=\frac{z-4}{2}=\mu ....(2)\end{array}$ $\mathrm{x}=4\mu +7,\mathrm{y}=3\mu +9,\mathrm{z}=2\mu +4$ $3\lambda -6=4\mu +7\Rightarrow 3\lambda -4\mu =13$ $\dots (3)\times 2$ $2\lambda =3\mu +9\Rightarrow 2\lambda -3\mu =9$ $\dots (4)\times 3$ $\begin{array}{c}6\lambda -8\mu =26\\ 6\lambda -9\mu =27\\ -+-\\ \mu =-1\end{array}$ $\begin{array}{c}\Rightarrow 3\lambda -4(-1)=13\\ 3\lambda =9\\ \lambda =3\end{array}$ int. point $(3,6,2);(7,8,9)$ ${\mathrm{d}}^2=16+4+49=69$ Ans. ${\mathrm{d}}^2+6=69+6=75$