Let $\;A (2 , 3 , 5)\;,B(-1 ,3 , 2)\;$ and $\;C(\lambda , 5 , \mu)\;$ be the vertices of a $\;\bigtriangleup ABC\;$ . If the median through A is equally inclined to the coordinate axes , then :

Question

$(a)\;5 \lambda - 8 \mu =0\qquad(b)\;8 \lambda - 5 \mu =0\qquad(c)\;10 \lambda - 7 \mu =0\qquad(d)\;7 \lambda - 10 \mu =0$