Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Since $\mathrm{AD}$ is the median
$$\therefore \mathrm{D}=\left(\frac{\lambda -1}{2},4,\frac{\mu +2}{2}\right)$$ Now, dR's of AD is $$a=\left(\frac{\lambda -1}{2}-2\right)=\frac{\lambda -5}{2}$$ $$b=4-3=1,c=\frac{\mu +2}{2}-5=\frac{\mu -8}{2}$$ Also, $a,b,c$ are $\mathrm{dR}$ 's $\therefore a=kl,b=km,c=kn$ where $l=m=n$ and $l^2+m^2+n^2=1$ $$\Rightarrow l=m=n=\frac{1}{\sqrt{3}}$$ Now, $a=1,b=1$ and $c=1$ $\Rightarrow \lambda =7$ and $\mu =10$