JEE Main 2014 (Online) 11th AprilQuestion 1
Let $A(2,3,5)$, $B(-1,3,2)$ and $C(\lambda,5,\mu)$ be the vertices of a $\triangle ABC$. If the median through $A$ is equally inclined to the coordinate axes, then :
3D Geometry
Solution
Midpoint of $BC$ is $\left(\frac{\lambda-1}2,4,\frac{\mu+2}2\right)$; direction from $A$ is $\left(\frac{\lambda-5}2,1,\frac{\mu-8}2\right)\propto(1,1,1)$, so $\lambda=7,\mu=10$ and $10\lambda-7\mu=0$.