JEE Main 2016 (Online) 10th AprilQuestion 1
$ABC$ is a triangle in a plane with vertices $A(2,3,5)$, $B(-1,3,2)$ and $C(\lambda,5,\mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $\left(\lambda^{3}+\mu^{3}+5\right)$ is
3D Geometry
Solution
Median direction $\left(\frac{\lambda-5}2,1,\frac{\mu-8}2\right)\propto(1,1,1)$ gives $\lambda=7$, $\mu=10$; so $\lambda^3+\mu^3+5=343+1000+5=1348$.