In a triangle ABC, $A=\left(2,3,5\right),B=\left(-1,3,2\right),C=\left(\lambda ,5,\mu \right).$ If the median through ‘A’ is equally inclined with axes then $\left(\lambda ,\mu \right)=$

$$\begin{gathered} Given points are \\ A(2,3,5),B(-1,3,2),C(\lambda ,5,\mu ) \end{gathered}$$

D= mid point g $BC=\left(\frac{\lambda -1}{2},4,\frac{\mu +2}{2}\right)$

$$\begin{gathered} \mathrm{D}.\mathrm{r}\text{ 's of }\overline{AD}=(\frac{\lambda -1}{2}-2,4-3,\frac{\mu +2}{2}-5) \\ =(\frac{\lambda -5}{2},1,\frac{\mu -8}{2}) \\ \sin ce median through A makes equal angles with coordinate axes then \\ \Rightarrow \frac{\lambda -5}{2}=1=\frac{\mu -8}{2} \\ \Rightarrow \frac{\lambda -5}{2}=1 and \frac{\mu -8}{2}=1 \end{gathered}$$

$\Rightarrow \lambda =7,\mu =10$