Question

Let ABC be a triangle with vertices at points $A(2,3,5),B(-1,3,2)$ and $C(\lambda ,5,\mu )$ in three dimensional space. If the median through A is equally inclined with the axes, then $(\lambda ,\mu )$ is equal to :

• A. $(10,7)$
• B. $(7,5)$
• C. $(7,10)$
• D. $(5,7)$

Answer 1

The correct option is C $(7,10)$

$\begin{array}{c}DisthemidpointofBCcoordinatesof\\ D=\left(\frac{\lambda -1}{2},4,\frac{\mu +2}{2}\right)\\ directionratiosofAD\\ \frac{\lambda -5}{2},1,\frac{\mu -8}{2}\\ forequalinclinationalltheseshouldequal\\ \frac{\lambda -5}{2}=1=\frac{\mu -8}{2}\\ \lambda =7,\mu =10\end{array}$